Should I Become a Mathematician?

In summary, to become a mathematician, you should read books by the greatest mathematicians, try to solve as many problems as possible, and understand how proofs are made and what ideas are used over and over.
  • #3,256
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  • #3,257


the big minus to the MAA site is that

a. they only put books up to 1991, newer stuff you need membership or read the magazine in the library to look stuff up...

b. older stuff - if it's out of print and old, they sometimes junk it off the list, which i think is a big minus.. they keep plenty on, but i think it's not enough...If one could access their older lists and newer lists, it would be one of the better ones... though sometimes they do recommend fads like some of the odd computer aided textbooks, or radical experiments [some good, some awful]...

but the MAA list is something that matches Parke's work almost perfectly... though it doesn't get into Physics, Engineering, Chemistry, Electronics...

you don't see Welchons+Krickenberg of the 50s, Dolciani of the 60s, or Munem of the 80s... for algebra...

but you'll get Three stars for the Demana Graphing Calculator books that were a fad..

-------

I just felt that it was a real letdown that the algebra aka
[school mathematics and Precalculus] parts of the list didnt include more titles, older out of print ones and some of the new ones...

like a huge gap of the 1970s...

--------------

Only two 1960s textbooks?
Only two 1970s textbooks?
come on!

and then the list starts rolling from 1981-1991

1960s
-------
- Allendoerfer, C.B. and Oakley, C.O. Fundamentals of Freshman Mathematics, New York, NY: McGraw-Hill, 1965. Second Edition.

- Ayre, H.G.; Stephens, R.; and Mock, G.D. Analytic Geometry: Two and Three Dimensions, New York, NY: Van Nostrand Reinhold, 1967. Second Edition

1970s
-------
- * Usiskin, Zalman. Advanced Algebra with Transformations and Applications River Forest, IL: Laidlaw Brothers, 1976.

- Larson, Loren C. Algebra and Trigonometry Refresher for Calculus Students New York, NY: W.H. Freeman, 1979.

1980s
-------
- Devlin, Keith J. Sets, Functions, and Logic: Basic Concepts of University Mathematics New York, NY: Chapman and Hall, 1981.

- Simmons, George F. Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry Los Altos, CA: William Kaufmann, 1981.

---------------
- one 1965
- one 1967
- one 1976
- one 1979
- two 1981
---------------
- zero 1982 books
- one 1983 book
- three 1984 books
- one 1985 book
- zero 1986 books
- two 1987 books
- zero 1988 books
- four 1989 books [many are later editions of earlier ones]
- three 1990 books
- two 1991 books

you can see when the billionth edition fad came in the mid 1980s also...My issue is considering how crucial things are for the algebra and calculus crowd, it's the place that should be the least neglected...

But then again, i think all unis should offer algebra and chemistry and math and physics from ground zero...

I think that's how Jeremy Bernstein at Harvard got into physics, he didnt take a class before, and poof ended up with a degree... and he turned into one of the better 70s 80s pop science writers and then later an excellent author on Modern Physics [aka basics for Quantum Mechanics]------
the MAA list is creepy though
2 stars for Sherman Stein and Spivak...
[they offer 2 stars for Leithhold's algebra text but don't add his calculus text]
3 stars for thomas and finney
and 2 stars for Priestley's strange historical approach to calculus. [something Morris Kline wouldn't approve of]

ideally, i'd like to see a maa/Parke like list that shows things before during and after the new math... and sadly that's a black hole for recommending books. Some of the texts were pretty experimental and freaky, neat as a reference, awful as a first exposure...

according to the MAA the only books cool enough for three starts after the Parke era would be
a. Thomas and Finney's Calculus [the 1952 edition is in Parke before Finney joined]
b. Apostol
c. Saywer's book What is Calculus About? [NML - New Mathematical Library of the 1960s]
d. Demana's Precalculus a Graphing Approachanyone out there use or browse, Leithhold and Stein's stuff from the 70s?
 
  • #3,258
mathwonk said:
well those are really tough questions. you are at an elite school where very little hand holding goes on, i.e. everyone assumes you know what you want, and they throw the math at you in the best form they can manage, and let it sort itself out.

There are always better people, always. I have been at all kinds of schools, and when I dropped down from ivy schools to state schools i thought well maybe now i'll be the best one here. No, there were still better people, and there always are.

So the choice has to be based on how much you enjoy what you are doing.

If you were hopelessly outclassed and had no chance, of course you should drop out, but that is not at all the case, with your record.

a certain level of talent is needed as a prerequisite, but after that entry level qualifying exam, it is all about effort.

Mariogs379 said:
@mathwonk,

Bit of a specific question but I thought you might be a good source of advice. Here's my background/question:

Went to ivy undergrad, did some math and was planning on majoring in it but, long story short, family circumstances intervened and I had to spend significant time away from campus/not doing school-work. So I did philosophy but have taken the following classes:

Calc II (A)
Calc III (A)
Linear Alg. (B+)
ODE's (A)
Decision Theory (pass)
Intro to Logic (A-)

Anyway, I did some mathy finance stuff for a year or so but realized it wasn't for me. I'm now going to take classes at Columbia in their post-bac program but wanted to get your advice on how best to approach this.

They have two terms so I'm taking Real Analysis I in the first term and, depending on how that goes, Real Analysis II in the second term. I'm planning on taking classes in the fall semester as a non-degree student and was thinking of taking:

Abstract Algebra
Probability
(some type of non-euclidean geometry)

Anyway, here are my questions:

1) What do you think of my tentative course selection above?

2) How much do you think talent matters as far as being able to hack it if I ended up wanting to do grad school in math?

3) I'm also having a hard time figuring out whether math is a fit for me. By that, I just mean that I really like math, I'm reading Rudin / Herstein in my free time, but I've spoken with other kids from undergrad and it's clear that they're several cuts above both ability and interest-wise. Any thoughts on how to figure this out?

Thanks in advance for your help, much appreciated,
Mariogs


Hey Mathwonk,

I finished the analysis class (using Rudin). Really interesting stuff though it's made me wonder whether I'm talented enough for more math. I ended up getting a B in the class but had to put a TON of time to get even that. Having said that (and maybe this is silly), I feel like Rudin must be discouraging for a lot of people. Had we used Abbott, I think I'd feel more confident about my abilities.

So:

1) Thoughts on this: http://www.brandeis.edu/departments/mathematics/graduate/certificate.html

2) I LOVED the cardinality stuff / Cantor's uncountability of the reals; though I don't know that analysis is something I'd want to do a ton more of. The reading I've done on my own makes me think algebra/topology is awesome, though!

I guess this question is vague but should I just do the Brandeis program and then I'll really know whether more math is for me? Seems like maybe my interest level in analysis isn't reflective of my interest in math more broadly...

It's probably the only thing where I feel like you *really* begin to understand things instead of just being spoonfed answers or formulas.

Thanks again for all your help on this!
 
  • #3,259


dustbin said:
I really like the book now. At first I found it very challenging because I knew nothing of what the opening material is on (proof and logic)... **Removed Text** ...If you have no knowledge of logic or proofs, it may help to start out with a book that explains the subject in more depth. If you have some familiarity... I say start with this.

Hope this helps!

Yes, thanks dustbin that was really helpful, I guess I have pretty similar math backround to you.
And actually the book came today, little earlier than I expected. Funny thing I noticed on the cover was that the book is a gift from the US.

It says: "This book has been presented to Finland by the government of the United States of America, under public law 265, 81st congress, as an expression of the friendship and good will which the people of the United States hold for the people of Finland."

So it's a little late but thanks guys! (I guess most/many posters are from US.)

dustbin said:
You can also check out MAA's list for different subjects. Here is precalc/calc

http://mathdl.maa.org/mathDL/19/?pa=content&sa=viewDocument&nodeId=3226

They have a book on there that is also by Allendoerfer called "Fundamentals of Freshmen Mathematics." Anyone heard of it?

That looks really useful site, thanks.
 
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  • #3,260


"Hey Mathwonk,

I finished the analysis class (using Rudin). Really interesting stuff though it's made me wonder whether I'm talented enough for more math. I ended up getting a B in the class but had to put a TON of time to get even that. Having said that (and maybe this is silly), I feel like Rudin must be discouraging for a lot of people. Had we used Abbott, I think I'd feel more confident about my abilities."

a B in a rudin class is a strong affirmation of your ability. congratulations!
 
  • #3,261


heh, would be surprised if math grad schools thought so...haha. I just picked up Mendelson's "Intro to Topology" and Munkres' book. Looks like really interesting stuff.

Think I should just go for that Brandeis program?

Thanks again for the help!
 
  • #3,262


the brandeis program looks good to me. i myself went to brandeis right out of college and the excellent teaching there made me realize i did enjoy math, and that math was even more interesting than i had thought. I learned far more in the environment there than I had as a Harvard undergrad, although Harvard's program is wonderful too, especially now. In fact Alan Mayer, the brilliant professor who first magnetized me to algebraic geometry, is still at Brandeis. I recommend you check it out.
 
  • #3,263


What'd you do at Brandeis?

Thanks again for the help.

Sounds like I should take a little math this spring. Maybe just abstract algebra? Or throw in a topology class too?
 
  • #3,264


RJinkies said:
Allendeorfer and Oakley - Principles of Mathematics

There's a Third Edition 1969 McGraw-Hill

and some of the books might be with title changes so the diffences could be minor or substantial...
in the day it was likely the same book tweaked for college students...Allendoerfer & Oakley - Principles of Mathematics - McGraw-Hill 1ed 1955 - 540? pages
Allendoerfer & Oakley - Principles of Mathematics - McGraw-Hill 3ed 1969 - 705? pages
Allendoerfer & Oakley - Fundamentals of Freshman Mathematics. McGraw-Hill 1959
Allendoerfer & Oakley - Fundamentals of College Algebra. McGraw-Hill 1967
I'm interested of the content in "Principles of Mathematics"; I have googled for a detailed table of contents, but can't seem to find any. I would love to read a more in-depth review of the book as well. So if anyone know of any, I would love it if you shared! :)

Also, "Fundamentals of Freshman Mathematics", is that one similar to the above mentioned book? On Google Books, one can read the following about the book:

"Survey of mathematics designed to prepare the student for a course in analytic geometry and calculus."

Sounds like a precalculus book, just like "Principles"?
 
  • #3,265


my guess as i hinted in that messages was i think Allendoerfer just wrote the same books three times, and revised half of them for 15 years too...

being one of the larger figures in the New Math, he just wanted to add some of the 'new ideas' that program was doing in the 50s and 60s

so i'd think a chapter on formalism and lite set theory stuff trying to add some Modern Algebra glitter to the people just starting off in math... [which may or may not be such a good thing]

just plop 1-2 extra chapters or tighten up the first few chapters so it's got harder problems for college math people [where it's rehashing algebra 12 and extras], you know stuff that might not be great to plop down on grade 10-11 students.

just gear the text for people 1-3 years older...
or it's quite likely that chapters get dropped for some titles, and added for the others, and the core book is the same...

all i know for sure is he added 150 extra pages in 15 years...
which could be 4 extra chapters...

My guess:
a. he only did one algebra book, 3 different ways and at least 5 different editions...
b. and he did a calculus book which was less of a splash..
c. Seattle probably has tons of copies at the uni library and I'm closer than you are, if one of us starts synchronizing our watches now...

with a lot of these things, seeing the actually book reviews like in the College Mathematics Journal or the American Physics Teacher and the AJP i think is where lots of the 30s 40s 50s 60s and early 70s books are hiding...

would be cool if someone had a website and showed photos of the books and what some of the praise or criticism was... Allendorfer, Krickeberger, Dolciani, the Courant-Fritz John set... or things like Resnick, Symon PSSC etc etc...

i wonder if Parke kept going on for another 10-20 years and took interest in SMSG and PSSC and how it created a kick start of new and *sometimes* better books after his list... sadly he seemed in a rush to get it out for 1957 and i think half of the 1956 year he looked a most things, and sometimes dropped a Dover title of ike a Russian book that will be out in 1-2 years..or a turn of the century reprint...his priority was his rather busy consulting practice in Mass as an Applied Mathematician with a good 2000+ reference books...

[actually he said that for professional type science people that if a book though it seems pricey if it can save you a day's wasted work, it paid for itself...though that's not really true for students, is it.. lol]

sure wonder what he thought of those programs in his old age.

Morris Kline did slam a lot of stuff with his books why johnny can't add and why the professor can't teach... but i do remember i wasnt all that hyped about his calculus text, and then at the time, Apostol didnt grip me either...[it seemed like a near impossibility to do that many pages in a semester i thought, and well, it's pretty dense, it's pretty hard and lots of proofs, Courant though murky seemed way more accessible, but you sure can't pick up lots of stuff easily or quickly...

[which you can from Thomas and Finner, or Sherman Stein, or JE Thompson or Syl Thompson... or hell, Granville Longley and Smith...]

GLS seemed like the nicest text to breeze through at the library, and so was Courant-John as the two texts, i'd most likely 'oops i lost it' excuses out of a pile of really BLAND 70s calculus texts...

oh a 60s McGraw-Hill -Calculus for Electronics

three calculus books got the thumbs up from me back in the day...along with Feynman's Lectures and the Berkeley Series... I didnt see any great high school or first year physics books that stood out

but i thought the best two texts then were
a. PSSC
b. Frederick J. Bueche's College Physics for Scientists and Enginners
1969 edition [i think it had another title] , 1974 edition 1981 edition, roughly... there was one more 4th edition for sure but i think the look of the book went downhill...

one of the more relaxed and precisely worded texts around. He thought the basics should be really well done, thought it was a top book of the 70s 80s though probably too hard for high school, too easy for some Uni-ersity Physics courses...

Bueche did one schaum's outline, what it was i can't recall [I don't think it was the College Physics one about 1938, or maybe in the 50s he was the editor?] But i think he was a big cheese at the Uni of Dayton in Ohio [Ohio State and Case Western i think are the two main physics places though]

there was also some 50s 60s Addison Wesley books on College Math too, if i recall, it could have Kaplan, who wanted to do an easier book after his higher up calculus text of the 40s 50s..

one author i can't recall,had like a pretty stuff 1950s Trigonometry book that was about 150 pages, it was pretty stiff reading and though a bit difficult, pretty stimulating and seemed like a popular way of doing things for the people after high school and wanted that one scary math class for liberal arts... anyways that author i think did a pre cal book/college math book and a calculs book too.

i think his trig book was circa 54 with Add-Wes but the 'other titles' splash was circa 60-61 if i recall. Two years ago, i knew where that book was *grin*...
 
  • #3,266


Dowland said:
I'm interested of the content in "Principles of Mathematics"; I have googled for a detailed table of contents, but can't seem to find any. I would love to read a more in-depth review of the book as well. So if anyone know of any, I would love it if you shared! :)

Also, "Fundamentals of Freshman Mathematics", is that one similar to the above mentioned book? On Google Books, one can read the following about the book:

"Survey of mathematics designed to prepare the student for a course in analytic geometry and calculus."

Sounds like a precalculus book, just like "Principles"?
Here is table of contents of Allendoerfer's and Oakleys Principles of Mathematics first edition (1955):Preface

List of Symbols

Chapter 1. Logic (p. 1-38)

1. Introduction
2. Definitions
3. Propositions
4. Propositions in Mathematics
5. Quantifiers
6. Symbols
7. Truth Tables
8. Applications of Truth Tables
9. Negation
10. Implications Derived from Other Implications
11. Mathematical Terminology
12. Methods of Proof
13. Methods of Proof (continued)

Chapter 2. The Number System (p. 39-68)

1. Introduction
2. Addition of Real Numbers
3. Multiplication of Real Numbers
4. Formal Properties of Real Numbers
5. Special Properties of Real Numbers
6. Special Properties of Zero
7. Special Properties of Integers
8. Special Properties of the Rational Numbers
9. Decimal Expansion
10. Some Irrational Numbers
11. Geometrical Representation of Real Numbers
12. The Use of Real Numbers in Plane Geometry
13. Distance between Two Points
14. Complex Numbers
15. Solutions of Other Algeabraic Equations
16. Classification of Numbers
17. Congruences

Chapter 3. Groups (p. 69-82)

1. Introduction
2. Groups
3. Examples of Groups
4. Further Examples of Groups
5. Theorems about Groups

Chapter 4. Fields (p.83-102)

1. Introduction
2. Definition of a Field
3. Examples of Fields
4. Theorema based upon Group Properties
5. Additional Theorems
6. Solution of Equations
7. Solution of Quadratic Equations
8. Inequalities
9. Theorems Concerning Fractions
10. Exponents and Radicals

Chapter 5. Sets and Boolean Algebra (p. 103-123)

1. Introduction
2. Sets
3. Relations between sets
4. Union and Intersection of Sets
5. Complements
6. Boolean Algebra
7. The Boolean Algebra (0,1)
8. Electrical Networks
9. Design of Circuits
10. Quantifiers

Chapter 6. Functions (p. 124-158)

1. Functions
2. Special Functions
3. Relations
4. Notations for a Function
5. Rule, Domain, and Range
6. Algebra of Functions
7. Graph of a Function
8. Graph of a Relation
9. Inverse Function
10. Functions Derived from Equations

Chapter 7. Algebraic Functions (p. 159-181)

1. Introduction
2. Polynomial Functions
3. Rational Functions
4. Explicit Algebraic Functions
5. Graphs and Continuity
6. Properties of Polynomial Equations
7. Synthetic Division
8. Roots of Polynomial Equations
9. Rational Roots of Rational Polynomial Equations
10. Real roots or Real Polynomial Equations

Chapter 8. Trigonometric Functions (p.182-224)

1. General Definitions
2. Special Real Numbers
3. General Real Numbers
4. Range and Graph of Functions
5. Addition Theorems
6. Identities
7. Equations
8. Directed Angles
9. Trigonometric Function of Directed Angles
10. Right Triangles
11. Law of Sines
12. Law of Cosines
13. Inverse Functions
14. Complex Numbers

Chapter 9. Exponential and Logarithmic Functions (p.225-235)

1. Introduction
2. Exponential Functions
3. The number "e"
4. Logarithmic Functions
5. Graphs
6. The Logarithmic Scale

Chapter 10. Analytic Geometry (p.242-283)

1. Introduction
2. Mid-point of a Line Segment
3. Directed Line Segment
4. Inclination, Slope, Direction Cosines
5. Angle between Two Directed Lines
6. Applications to Plane Geometry
7. The Straight Line
8. Conic Sections
9. The Circle
10. The Parabola
11. The Ellipse
12. The Hyperbola
13. Applications
14. Polar Coordinates
15. Polar Coordinates Continued
16. Parametric Equations

Chapter 11. Limits (p. 284-329)

1. Introduction
2. Historical Notes
3. Sequences
4. Limits of Sequences
5. Examples of Sequences
6. Theorems of Limits of Sequences
7. Series
8. Limits of Functions
9. Theorems of Limits of Functions
10. Continuity
11. Area
12. Rates
13. Tangent to a Curve

Chapter 12. The Calculus (p. 330- 363)

1. Integration
2. Differentiation
3. Comparison of Integration and Differentiation
4. Rules of Differentiation
5. Second Derivatives
6. Maxima and Minima
7. Related Rates

Chapter 13. Statistics and Probability (p. 364-420)

1. The Nature of Statistics
2. Sampling
3. Presentation of Data
4. Frequency Distributions
5. Characteristics of Frequency Distributions
6. Grouping
7. Averages
8. Interpretation of the Mean
9. Computation of the Mean
10. Standard Deviation
11. Probability
12. Permutations
13. Combinations
14. Binomial Theorem
15. Probability (Again)
16. Empirical Probability
17. Expectation
18. Repeated Events
19. Binomial Distribution
20. Testing Hypothesis
21. Cumulative Normal Curve
22. Normal Distribution
23. Normal Distribution (continued)
24. Distribution of Sample Means
25. The Logical Roles of Statistics

Answers to Selected Exercises

IndexI can't really give in-depth review since I have not yet started studying it, but it seems to be good
"bridge" from basic algebra/geometry/trigonometry/calculus knowledge to higher mathematics.

I'm getting little ahead of myself, but when I'm done with Allendoerfer I will probably get Apostol's Calculus Books.
 
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  • #3,267


sounds like a high school honours course pretty much, or close to a college algebra like class, which got phased out with the space race, they wanted no longer to teach a review of high school and then push you into calculus, but just push you into calculus... and push out more engineers quicker.. and now there's the trend to push calculus into the high schools and then you really zoom into accelerated stuff into uni...

I think in the earlier days when there was less textbook competition and less crowded unis, you were always better off when a school could teach the most basic of math, or chemistry or physics, if you lacked anything, and the college professors would use better textbooks and it would mesh more with their calculus programs...

one thing i know, that if you take a math or chemistry course where you start on chapter 8 in the first week of classes, it would probably be better to read the first 7 chapters a semester or year earlier, and not miss out on the authors usually well-constructed development.

sometimes the stuff a chemistry book assumes, it's likely you might not have down any of those problems or concepts for 20% of things... and if you just skirted it, you're probably conceptionally shaky that you wouldn't notice somethng, unless it was pointed out to you...

the interesting thing, i found was with a lot of books, algebra texts with a strong new math feel, or books on diff eqs or complex variables, or some organic chem, that *often* chapter 1 where it's suppossedly review, is actually much harder than the new material with chapters 2 and 3...

had an interesting talk with my math teacher about that phenomenon... but i think it was more that sometimes in the 70s kids are less better prepared, and i think the textbook changes and curriculum changes had a fair deal to do with that...

I think i'd cringe at the first 150 pages of allendorfer though, but if it's a slow enough pace, or a second dip into algebra, you can enjoy it a lot more...

I'm guessing that it's probably one of the earlist books in spirit to the new math [before it started AFTER sputnik], without trying to cram too much Bourbaki down the throats of 16 year olds

the PSSC program was Before Sputnik, but the SMSG New math stuff was in reaction to sputnik...

and the Seaborg CHEM books from 1964 are great reading, but I think a lot of the problem solving skills are hidden or absent, or at that time, really pushed in first year chem... things seems a bit more leisurely for chemistry in the days of slide rules for chemistry 11 once upon a time...

sad thing is more all those 60s chemistry texts shows hints of the most exciting stuff going on, and they yanked all that stuff out by the 70s

------

think about using Sylvanius Thompson and JE Thompson's
Calculus Made Easy and Calculus made Simple [1910s and 1930s]
[or Sherman Stein]
if you are going to read Apostol or Spivak

i find an easy book is great parallel reading...
 
  • #3,268


The above table of contents looks, as far as I can tell, exactly like the one in my first edition copy of Principles of Mathematics. So it appears that only their titles may be different? Pretty much all of the page numbers are the same as well (I could only find one or two that were different on the ToC).

RJinkies said:
I think i'd cringe at the first 150 pages of allendorfer though, but if it's a slow enough pace, or a second dip into algebra, you can enjoy it a lot more...

The chapters on logic were the hardest for me (completely new subjects to me). I did the first 4 chapters, took a break to study a book that focused more on this material in particular, and then came back to it (and re-did it). After my second run-through with it, I handled it very well. The first time, I indeed did work very slowly through it. After coming back to it and going through those chapters again, the subsequent chapters (I've done up to the calculus topics, but not including them) have been much more gentle.
 
  • #3,269


ovael said:
Here is table of contents of Allendoerfer's and Oakleys Principles of Mathematics first edition (1955):


Preface

List of Symbols

Chapter 1. Logic (p. 1-38)

1. Introduction
2. Definitions
3. Propositions
4. Propositions in Mathematics
5. Quantifiers
6. Symbols
7. Truth Tables
8. Applications of Truth Tables
9. Negation
10. Implications Derived from Other Implications
11. Mathematical Terminology
12. Methods of Proof
13. Methods of Proof (continued)

Chapter 2. The Number System (p. 39-68)

1. Introduction
2. Addition of Real Numbers
3. Multiplication of Real Numbers
4. Formal Properties of Real Numbers
5. Special Properties of Real Numbers
6. Special Properties of Zero
7. Special Properties of Integers
8. Special Properties of the Rational Numbers
9. Decimal Expansion
10. Some Irrational Numbers
11. Geometrical Representation of Real Numbers
12. The Use of Real Numbers in Plane Geometry
13. Distance between Two Points
14. Complex Numbers
15. Solutions of Other Algeabraic Equations
16. Classification of Numbers
17. Congruences

Chapter 3. Groups (p. 69-82)

1. Introduction
2. Groups
3. Examples of Groups
4. Further Examples of Groups
5. Theorems about Groups

Chapter 4. Fields (p.83-102)

1. Introduction
2. Definition of a Field
3. Examples of Fields
4. Theorema based upon Group Properties
5. Additional Theorems
6. Solution of Equations
7. Solution of Quadratic Equations
8. Inequalities
9. Theorems Concerning Fractions
10. Exponents and Radicals

Chapter 5. Sets and Boolean Algebra (p. 103-123)

1. Introduction
2. Sets
3. Relations between sets
4. Union and Intersection of Sets
5. Complements
6. Boolean Algebra
7. The Boolean Algebra (0,1)
8. Electrical Networks
9. Design of Circuits
10. Quantifiers

Chapter 6. Functions (p. 124-158)

1. Functions
2. Special Functions
3. Relations
4. Notations for a Function
5. Rule, Domain, and Range
6. Algebra of Functions
7. Graph of a Function
8. Graph of a Relation
9. Inverse Function
10. Functions Derived from Equations

Chapter 7. Algebraic Functions (p. 159-181)

1. Introduction
2. Polynomial Functions
3. Rational Functions
4. Explicit Algebraic Functions
5. Graphs and Continuity
6. Properties of Polynomial Equations
7. Synthetic Division
8. Roots of Polynomial Equations
9. Rational Roots of Rational Polynomial Equations
10. Real roots or Real Polynomial Equations

Chapter 8. Trigonometric Functions (p.182-224)

1. General Definitions
2. Special Real Numbers
3. General Real Numbers
4. Range and Graph of Functions
5. Addition Theorems
6. Identities
7. Equations
8. Directed Angles
9. Trigonometric Function of Directed Angles
10. Right Triangles
11. Law of Sines
12. Law of Cosines
13. Inverse Functions
14. Complex Numbers

Chapter 9. Exponential and Logarithmic Functions (p.225-235)

1. Introduction
2. Exponential Functions
3. The number "e"
4. Logarithmic Functions
5. Graphs
6. The Logarithmic Scale

Chapter 10. Analytic Geometry (p.242-283)

1. Introduction
2. Mid-point of a Line Segment
3. Directed Line Segment
4. Inclination, Slope, Direction Cosines
5. Angle between Two Directed Lines
6. Applications to Plane Geometry
7. The Straight Line
8. Conic Sections
9. The Circle
10. The Parabola
11. The Ellipse
12. The Hyperbola
13. Applications
14. Polar Coordinates
15. Polar Coordinates Continued
16. Parametric Equations

Chapter 11. Limits (p. 284-329)

1. Introduction
2. Historical Notes
3. Sequences
4. Limits of Sequences
5. Examples of Sequences
6. Theorems of Limits of Sequences
7. Series
8. Limits of Functions
9. Theorems of Limits of Functions
10. Continuity
11. Area
12. Rates
13. Tangent to a Curve

Chapter 12. The Calculus (p. 330- 363)

1. Integration
2. Differentiation
3. Comparison of Integration and Differentiation
4. Rules of Differentiation
5. Second Derivatives
6. Maxima and Minima
7. Related Rates

Chapter 13. Statistics and Probability (p. 364-420)

1. The Nature of Statistics
2. Sampling
3. Presentation of Data
4. Frequency Distributions
5. Characteristics of Frequency Distributions
6. Grouping
7. Averages
8. Interpretation of the Mean
9. Computation of the Mean
10. Standard Deviation
11. Probability
12. Permutations
13. Combinations
14. Binomial Theorem
15. Probability (Again)
16. Empirical Probability
17. Expectation
18. Repeated Events
19. Binomial Distribution
20. Testing Hypothesis
21. Cumulative Normal Curve
22. Normal Distribution
23. Normal Distribution (continued)
24. Distribution of Sample Means
25. The Logical Roles of Statistics

Answers to Selected Exercises

Index


I can't really give in-depth review since I have not yet started studying it, but it seems to be good
"bridge" from basic algebra/geometry/trigonometry/calculus knowledge to higher mathematics.

I'm getting little ahead of myself, but when I'm done with Allendoerfer I will probably get Apostol's Calculus Books.
Thank you, ovael! Chapters 1,3,4,5 looks very interesting!

I was actually thinking of buying it, because I've heard such good things about here on PF. But I'm currently doing "Basic Mathematics" (Serge Lang), "Elementary Algebra" (Harold Jacobs) and "Algebra" (Gelfand) at the same time, and in parallell to my ordinary high school curriculum, so I think it will be pretty overwhelming and unnecessary with another book.

However, good luck with your studies now, ovael! And I'm looking forward to a review of the book sometime in the future. :)


(BTW, sorry for any language errors, English is not my native.)
 
  • #3,270


dustbin - The chapters on logic were the hardest for me (completely new subjects to me). I did the first 4 chapters, took a break to study a book that focused more on this material in particular, and then came back to it (and re-did it). After my second run-through with it, I handled it very well. The first time, I indeed did work very slowly through it. After coming back to it and going through those chapters again, the subsequent chapters (I've done up to the calculus topics, but not including them) have been much more gentle.

What you experienced, is exactly how i think i would feel if i tackled him too! For me i remember people always finding Dolciani a hard text but if you read Modern Algebra Book 2 from 1964 from the start, it wasnt hard at all, but it got me to realize just how shaky our algebra was with a class with 2 textbooks and dolciani was only used 20% of the time, and just taking random stuff out of it...

I think i usually recommended Schaum's Outlnes [there were about 3 or 4] , Dolciani from the 60s or Munem from the 80s as the quickest fix or way to start off algebra...

I think that's one of the big reasons for the decline in math, we arent going slow enough and as thorough enough, and well we also need textbooks we can start beginning to end.

the more i looked at chemistry texts, i found that if you arent reading it from page one, you're really losing out on a solid foundation of the topic... one of the 1967 classics that was used at Caltech [it was a bright yellow one], the author basically started in on chapter 8 and ran through it.

He said that if you had zero chemistry before, and you could cram 3-4 months into reading that, or if you take the course and really really push it, you could basically coast through the course okay... I thought it was one of the finest textbooks since he listed all the great classics of the early and mid 60s at the end of each chapter, and you could end up with 40 textbooks from 1959-1966 on your reading list lol Why the subject lost most of its charm in the 70s, I'm not sure why but i think the focus narrowed and the enjoyable asides and well as deep explanations of the basics just went out the window... just push the mathematical essentials for what people need for organic or physical chem and forget the rest...
dowland - currently doing "Basic Mathematics" (Serge Lang), "Elementary Algebra" (Harold Jacobs) and "Algebra" (Gelfand) at the same time, and in parallell to my ordinary high school curriculum, so I think it will be pretty overwhelming and unnecessary with another book.

Lang seemed way more approchable with his basic math book and his old calculus book when he wanted to make a simplified course... lots of people don't appreciate his later stuff, till you're closer to grad school with linear and stuff, and a fair number of people get an allergy to him if they try to soak him in too soon. I was surprised when i came across his easier books and i was expecting a terse harsh introduction...

Jacobs did some good stuff with his elementary algebra and geometry books in the 70s 80s, one had an Escher artwork thing on it too... how do like Elementary Algebra by him, and i assume you got 1 of the 5 Green and White Birkhauser Gelfand books which probably go well with the NML series too...

Definately want to hear your thoughts on Lang and Jacobs algebra... i don't think many people at all pick or get dumped jacob's from the MAA list of recommended books for algebra anymore... but what what i recall it was always considered a great text for people with little or no background...i'm not sure if teacher's only picked it because of the Escher artwork or people listened to the MAA more lol
 
  • #3,271


RJinkies said:
idowland - currently doing "Basic Mathematics" (Serge Lang), "Elementary Algebra" (Harold Jacobs) and "Algebra" (Gelfand) at the same time, and in parallell to my ordinary high school curriculum, so I think it will be pretty overwhelming and unnecessary with another book.

Lang seemed way more approchable with his basic math book and his old calculus book when he wanted to make a simplified course... lots of people don't appreciate his later stuff, till you're closer to grad school with linear and stuff, and a fair number of people get an allergy to him if they try to soak him in too soon. I was surprised when i came across his easier books and i was expecting a terse harsh introduction...

Jacobs did some good stuff with his elementary algebra and geometry books in the 70s 80s, one had an Escher artwork thing on it too... how do like Elementary Algebra by him, and i assume you got 1 of the 5 Green and White Birkhauser Gelfand books which probably go well with the NML series too...

Definately want to hear your thoughts on Lang and Jacobs algebra... i don't think many people at all pick or get dumped jacob's from the MAA list of recommended books for algebra anymore... but what what i recall it was always considered a great text for people with little or no background...i'm not sure if teacher's only picked it because of the Escher artwork or people listened to the MAA more lol
Oops, I meant "Elementary GEOMETRY", not Algebra! I aksed earlier in this thread about the importance of learning euclidean geometry thouroughly and I got some mixed answers, but I finally decided to give it a try (can't hurt and one can always make some extra sparetime for mathematics right :))

As Regards to Lang's book, I love it! I have worked through approximately half of the book now and it has really given me a new way of looking at mathematics. Basic Mathematics is the first math book I've ever read at the side of the ordinary high school curriculum in my country, and it feels lika a completely different philosophy and attitude towards the subject and the student, which I think every high school student interested in mathematics should have the opportunity to expercience.

Can't write more for the moment, maybe I'll return with some more elaborated comments on the book.
 
  • #3,272


Damn, it's extremely difficult to find someone with an opinion of Jacobs Algebra text...

shame the MAA doesn't like any basic geometry books before 1968...

Geometry: School Geometry

Loomis, E. The Pythagorean Proposition - NCTM 1968
** Jacobs, Harold R. Geometry, New York, NY: W.H. Freeman, 1974 First Edition.
* Konkle, Gail S. Shapes and Perceptions: An Intuitive Approach to Geometry - Prindle, Weber and Schmidt 1974
* Moise, Edwin E. and Downs, Floyd L. Geometry - Addison-Wesley 1975
** O'Daffer, Phares G. and Clemens, Stanley R. Geometry: An Investigative Approach- Addison-Wesley 1976
* Bruni, James V. Experiencing Geometry - Wadsworth 1977
Kempe, A.B. How to Draw a Straight Line - NCTM 1977
* Fetisov, A.I. Proof in Geometry - MIR 1978
Hoffer, Alan. Geometry - Addison-Wesley 1979
Clemens, Stanley R.; O'Daffer, Phares G.; and Clooney, Thomas J. Geometry - Addison-Wesley 1983
** Jacobs, Harold R. Geometry, New York, NY: W.H. Freeman 1986. Second Edition.

one thing i hear about the 50s 60s geometry texts are they seem to be zombie-like. Some people seemed to like the challenge, but most anyone with high school geometry thinks its pretty useless if you take higher math classes...

as for Lang he gets the most praise for his easy books, but most of his stuff people don't like till they are in 4th year and like all that sterile bourbaki like formalism with linear.. Some people really dislike his book, but after a year or two then mellow and appreciate it more when get higher up...

so it was a shock for me when i found out lang did a great basic book, and once upon a time a pretty clear barebones calculus text...
 
  • #3,273


I have wanted to be a pure mathematician since I was about 15. I thought I was quite good at mathematics till I got to university and saw how talented some of my fellow classmates are. For instance many of them do no study besides attending class, and spend most of their time socialising/drinking/gaming yet still out perform me in many assesment tasks. This is quite frankly soul crushing as I spend most of my time thinking about mathematical things and it really highlights my lack of natural ability.

The thing is I still love the subject. Yet everytime one of my cocky friends tells me how well he has done in the latest exam or assignment I feel crushed and betrayed my the subject I love so much. I used to believe that genius was 90% Hardwork, but now I see that most of these sayings are just political correctness gone wrong.

Is it possible to even get a phd let alone tenure in pure mathematics when you lack that "spark" of genius?
 
  • #3,274


I have wanted to be a pure mathematician since I was about 15. I thought I was quite good at mathematics till I got to university and saw how talented some of my fellow classmates are. For instance many of them do no study besides attending class, and spend most of their time socialising/drinking/gaming yet still out perform me in many assesment tasks. This is quite frankly soul crushing as I spend most of my time thinking about mathematical things and it really highlights my lack of natural ability.

The thing is I still love the subject. Yet everytime one of my cocky friends tells me how well he has done in the latest exam or assignment I feel crushed and betrayed my the subject I love so much. I used to believe that genius was 90% Hardwork, but now I see that most of these sayings are just political correctness gone wrong.

Is it possible to even get a phd let alone tenure in pure mathematics when you lack that "spark" of genius?

I see you keep ignoring what I am telling you about knowing the tricks of the trade and of learning in general.

Part of your problem seems to be that you are thinking about different things than your friends. They problem just hit the homework and don't really question things, whereas you question things.

Here's one of the tricks I had up my sleeve in undergrad that I still use when I can, that, in particular, explains how I would avoid having to study much outside class sometimes (except to come up with my own explanations of things where necessary). I didn't take notes. Instead, during the lecture, I kept repeating what was said in the lecture up to that point in time in my mind. Always summarizing the lecture in my mind, while continuing to listen to the next part. A few things I didn't understand, I would set aside for meditating on later. After the lecture, I would go over it in my mind again. Sometimes, this meant I was already done studying after my session of reflection on the lecture was over. I would do it during the day while I was going about my business, eating, driving, etc. The usual rate of retention from lectures is 10%, whereas, if I concentrate, I can often recall 100% of the content (though not the specifics of how it was delivered). Even two years from now, if I so desire, just by a little review as necessary. If I wanted to, I could rehash the entire lecture. This would work best if the lecture was fairly conceptual in nature, and thus more memorable.

Another trick that I had was just reading Visual Complex Analysis. I think if someone reads it and understands a good portion of that book and its message, they would outperform someone with otherwise equal ability by a long shot in all their subsequent classes.
 
  • #3,275


homeomorphic said:
I see you keep ignoring what I am telling you about knowing the tricks of the trade and of learning in general.

Part of your problem seems to be that you are thinking about different things than your friends. They problem just hit the homework and don't really question things, whereas you question things.

Here's one of the tricks I had up my sleeve in undergrad that I still use when I can, that, in particular, explains how I would avoid having to study much outside class sometimes (except to come up with my own explanations of things where necessary). I didn't take notes. Instead, during the lecture, I kept repeating what was said in the lecture up to that point in time in my mind. Always summarizing the lecture in my mind, while continuing to listen to the next part. A few things I didn't understand, I would set aside for meditating on later. After the lecture, I would go over it in my mind again. Sometimes, this meant I was already done studying after my session of reflection on the lecture was over. I would do it during the day while I was going about my business, eating, driving, etc. The usual rate of retention from lectures is 10%, whereas, if I concentrate, I can often recall 100% of the content (though not the specifics of how it was delivered). Even two years from now, if I so desire, just by a little review as necessary. If I wanted to, I could rehash the entire lecture. This would work best if the lecture was fairly conceptual in nature, and thus more memorable.

Another trick that I had was just reading Visual Complex Analysis. I think if someone reads it and understands a good portion of that book and its message, they would outperform someone with otherwise equal ability by a long shot in all their subsequent classes.

Homeomorphic I am not ignoring you, I just cannot apply your techniques to my life. If I may say so you have an exceptional memory and mathematical ability, even if I do the things you mention it is to no avail. I cannot recall an entire lecture for the life of me, I will forget the intracies of a proof as soon as I finish reading it, regardless if it is in a book or on a blackboard. I think you just have the spark of genius which I spoke of, something I will never have, so there is no point in me trying to follow your advice (I have been trying over the last few days with no success). I wish I could just walk away from mathematics, to become a Doctor or an engineer or something less intellectually ambitious but whenever I have considered it, it has left me feeling empty.
 
  • #3,276


Group_Complex said:
I have wanted to be a pure mathematician since I was about 15. I thought I was quite good at mathematics till I got to university and saw how talented some of my fellow classmates are. For instance many of them do no study besides attending class, and spend most of their time socialising/drinking/gaming yet still out perform me in many assesment tasks. This is quite frankly soul crushing as I spend most of my time thinking about mathematical things and it really highlights my lack of natural ability.

The thing is I still love the subject. Yet everytime one of my cocky friends tells me how well he has done in the latest exam or assignment I feel crushed and betrayed my the subject I love so much. I used to believe that genius was 90% Hardwork, but now I see that most of these sayings are just political correctness gone wrong.

Is it possible to even get a phd let alone tenure in pure mathematics when you lack that "spark" of genius?

Every field requires a particular skillset where you need to have some kind of exceptional ability in a few particular things.

Everybody has particular things that they are good at: some are great at dealing with people and can understand what makes people tick but they are horrible at analyzing situations devoid of emotion or personality, while others can look at something objectively in a kind of brutally honest manner but may not really understand other people that well.

The point I'm trying to make is that there are many things that have different requirements and we do have quite a lot of different avenues to pursue.

If you are not exceptional in one thing and you don't go on to that thing, don't take it personally: find the place where you can really do your thing well and become good at that.

Also I want to say that if you are absolutely set on doing a particular thing, then just remember that you can be flexible and pursue the options that are very close to that thing so much that it's hard to differentiate in many respects.

There are tonnes of careers that utilize the same kinds of skills and provide the same kinds of work that the one you originally envisioned that you haven't already thought about, and you may be surprised at how enjoyable those may be.

I would talk to as many people as you can about different options and get a feel of the kinds of people and skills that they employ and consider those options that are as close to what you are set on so that at least these things give you something to think about.
 
  • #3,277


Homeomorphic I am not ignoring you, I just cannot apply your techniques to my life. If I may say so you have an exceptional memory and mathematical ability, even if I do the things you mention it is to no avail. I cannot recall an entire lecture for the life of me, I will forget the intracies of a proof as soon as I finish reading it, regardless if it is in a book or on a blackboard. I think you just have the spark of genius which I spoke of, something I will never have, so there is no point in me trying to follow your advice (I have been trying over the last few days with no success). I wish I could just walk away from mathematics, to become a Doctor or an engineer or something less intellectually ambitious but whenever I have considered it, it has left me feeling empty.

I may have an exceptional memory and good, but not great mathematical ability, but how did I get there? A lot of people outperform me in classes, too, all the time. True, in some of my undergrad classes, I was way ahead of anyone else. In grad school, I just feel retarded all the time, compared to the best students, and especially compared to the professors.

If reviewing stuff isn't working, try reviewing it every day. The key is that you have to practice remembering. The main concept is that if you want to remember, you have to try to recall things WITHOUT LOOKING. Actually, maybe it would be easier to try to apply some of things in subjects other than math first. In math, it's compounded by the difficulty of being able to conceptualize well. I don't know if you like languages. Try to just start small. Take one Spanish (or your favorite language) word, and try to focus on that one word. Just be determined that you will never forget it. Review it every day. You'll never forget it. I think everyone has the ability to put facts into long term memory. Think about it. There are some things you just don't forget. Why? What is it that makes those things memorable?

This might be an eye-opener.

http://www.ted.com/talks/joshua_foer_feats_of_memory_anyone_can_do.html

Note that this kind of memory isn't that useful in math because I think understanding is more important. However, it is a big hint as far as what is possible.
 
  • #3,278


chiro said:
Every field requires a particular skillset where you need to have some kind of exceptional ability in a few particular things.

Everybody has particular things that they are good at: some are great at dealing with people and can understand what makes people tick but they are horrible at analyzing situations devoid of emotion or personality, while others can look at something objectively in a kind of brutally honest manner but may not really understand other people that well.

The point I'm trying to make is that there are many things that have different requirements and we do have quite a lot of different avenues to pursue.

If you are not exceptional in one thing and you don't go on to that thing, don't take it personally: find the place where you can really do your thing well and become good at that.

Also I want to say that if you are absolutely set on doing a particular thing, then just remember that you can be flexible and pursue the options that are very close to that thing so much that it's hard to differentiate in many respects.

There are tonnes of careers that utilize the same kinds of skills and provide the same kinds of work that the one you originally envisioned that you haven't already thought about, and you may be surprised at how enjoyable those may be.

I would talk to as many people as you can about different options and get a feel of the kinds of people and skills that they employ and consider those options that are as close to what you are set on so that at least these things give you something to think about.

My interests are in academic mathematics, I would not be happy working in any other capacity.
 
  • #3,279


hi groupcomplex

- The thing is I still love the subject. Yet everytime one of my cocky friends tells me how well he has done in the latest exam or assignment I feel crushed and betrayed my the subject I love so much. I used to beliee that genius was 90% Hardwork, but now I see that most of these sayings are just political correctness gone wrong.

Well, there is exceptional talent, and then there are people who do put in 45 hours a week and get outstanding grades too, and then there are the other 80% of people...where anything can and does happen.

You can do 75% of anything the 'talented' people do, if you put in the hours, and slowly climb the ladder, mastering course after course... Mathwonk made some comments about this months ago, and i was quiet surprised at all the hope and enthusiasm he offered for people who struggle, or don't feel they got any natural talent for stuff. [Maybe someone can find the message number for that one]


Another thing is, for some of these students, they might seem leaps and bound ahead of you, but that isn't any guarantee they will be choosing math as a career or that they might do less well later on, or stop where you'll be taking way more math classes than they are. Depth is important, as well as knowing the ideas [especially in physics], and in some ways that may be more important than the problem solving long term, or talent.

And did these people read the subject beforehand? or do they just focus on the absolute minimum of essentials for good grades, with some talent and some studying...

here it could be they got a different box of tools, they got a toolkit months or years before you started yours in the first week of classes...

or they study differently and work the problems differently... or who knows...--------hi homeomorphic

- Here's one of the tricks I had up my sleeve in undergrad that I still use when I can, that, in particular, explains how I would avoid having to study much outside class sometimes (except to come up with my own explanations of things where necessary). I didn't take notes. Instead, during the lecture, I kept repeating what was said in the lecture up to that point in time in my mind. Always summarizing the lecture in my mind, while continuing to listen to the next part. A few things I didn't understand, I would set aside for meditating on later.

I knew one math teacher, who actually said for people to stop scribbling with notetaking and just follow his lectures and absorb it, and he said that he'd be following the textbook closely so there's no need for 'notes'. He didnt say that to all his classes though...

As long as you're reading the book and doing the problems, i think it should work...
It wouldn't work in classes with 'no text' like in the days of Oppenheimer's Quantum courses where people were rushing to copy down the blackboard and it was near impossible to catch up before he would erase stuff and go on...[Schiff's book in the 40s 50s was said to be largely based on those] Those were the days of notetaking!

Personally i think in many cases, notetaking is done, because the teacher didnt pick a deep enough textbook, or he didnt add 1-3 other supplementary texts to make that unnecessary, or he didnt toss out photostats of outlines and notes and summaries to his classes so they don't *need* to take notes.

Often i would find that there was a 50s 60s or 70s textbook that explained things more like the teacher's style and if you browsed that book with the 'curriculum/syllabus gunk', you'd probably get 70% more out of the damn class.

Where there are 'notes' there is somewhere in the uni-curse, an older textbook that said it better and waaaaaaaay less sloppy!and some classes, are geared where the teacher wants to 'demonstrate' and then you read the text, and a lot of others where you read pages xx to xx, and then you come to class.
 
  • #3,280
try not to get suckered by that game of " my friend never studies but got a higher score than me".

so what? do the subject for the joy of learning it. if need be make some new friends with a better attitude toward learning.

and eventually those people who do not study will fail, no matter how brilliant.
 
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  • #3,281


@mathwonk,

1) Do you think Brandeis being a "lesser" math dept. should be a concern re: their certificate program?

2) Thoughts on the math GRE? It sounds like that's pretty relevant given that it provides some kind of objective measure, no?

3) Thoughts on what I could do during the 9 months between applying to grad school and matriculating?

Thanks again for all the help,
Mariogs
 
  • #3,282


Has anyone worked with any of K.A. Stroud's texts? Particularly, I'm asking about his Vector Analysis text.
 
  • #3,283


I think there's 12 books in the Stroud and Booth and they use the 1960s Programmed Instruction style of teaching [which half the time is done right]

Engineering Mathematics came out about 1970 and it's like in a fifth and sixth edition recently, and I'm not sure if the artwork or newest changes are for the better...

-------
some comments in my notes

[both Engineering Mathematics and Advanced Engineering Mathematics are a great help for Differential Equations in ways Boyce and DiPrima are not]

[remarkable work]

[I have studied numerous mathematics texts, and I can say with absolute certainty that this is the finest mathematics text I have ever found.Unlike virtually every other technical math book out there(calculus, differential equations, integral equations, statistics etc)this book provides more than the dreary, boring, purely analytic approach (algebra,limits etc) that tends to practically wipe out true understanding. In my calculus class I hear questions whose answers are extremely masked by the highly esoteric mathematical bull@#$@, but which present themselves so easily with a simple picture. This book provides those pictures, but more remarkably it is written in such a way that people want to work through it - compared to those other books. In addition, this book has been shown (via experimentation) to significantly increase test scores - compared to standard lecture approach.]

---------
Linear Algebra
Differential Equations
Vector Analysis - 2005 - 448 pages
Complex Variables
Engineering Mathematics - Sixth Edition - 1200 pages
Advanced Engineering Mathematics - Fourth Edition - 1280 pages
Essential Mathematics for Science and Technology/Foundation Mathematics
Further Engineering Mathematics
Laplace Transforms
Fourier Series and Harmonic Analysis
Mathematics for Engineering Technicians
Engineering Mathematics Through Applications - Kuldeep Singh [only book in the series not written by Stroud and Booth]
---------
so it's a set of 12 books which started in 1970...

and from what i gather, it belongs up there with Schaums, and REA, and now Stroud...
--------

There was an early early 70s [seemed about 1967-1971] that was a paperback 5 Volume set on learning calculus by programmed instruction i saw once in the library that looked great, anyone remember the author, or the publisher, exact name, or hell, comments about that one?

programmed instruction books are rare, some are well done, and it's really a lot of work to do it properly, and i always cringe when people say oh computers do it better and stuff, but stroud is one of the better ones out there that is still in print, and still well liked.

i got one spiral bound one for electrodynamics for like a physics 12 or college physics course, but i aint seen any others...Hope this is helpful...

can't offer a detailed criticism though...
 
  • #3,284
Brandeis a "lesser" math dept? lesser than what? it certainly offered me more than i could handle from Monsky, Mayer, Brown, Buchsbaum, Palais, Matsusaka, H. Levine, J. Levine, Rossi, Auslander, Seeley, Spivak, Sherman, Wells, Vasquez, ...and I have no reason to believe it has slipped from those days, even if I do not personally know most of the young people there today. It is ranked around #40 by US News but the problem with such rankings is that Brandeis is better as a math dept than US News is as a magazine.
 
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  • #3,285


Does anyone have a list of undergrad textbooks used at Brandeis?
I didnt see much of a syllabus offered to 'non-students'...

It's always a shame since i always judge schools by how 'accessible' their syllabus is and how far back they show it, or keep their old course stuff 'online'... It's always been a surprise for years now on the web that schools and teachers always wipe the old slates clean and then put up the ominous:
'Textbook: TBA'

I'm always on the search for schools where they use older oddball textbooks, or dump a ton of "suggested" texts after the one required one...For me, the syllabus is the key to it all, if i get funny vibes, i run for the hills...
once you got that, then i think the teachers, school reputation, etc etc counts.
For others, most any texts will do, as long as you get dumped with 'extra' homework and challenges... [which i think works maybe for the higher up classes...]
 
  • #3,286


Well take it with a grain of salt, but in my spare time a whlle i mixed up a bunch of rankings for unis just for my own fun...

anyhoo Brandeis is probably in the top 40 schools for higher math...for people who like lists...
here we go:
201 Brandeis University - Waltham, MA
[#64 Top End Physics]
[#40 Top End Mathematics]
[#68 Chemistry Top End]

------
8 Princeton University - [#1 Top End Mathematics]
1 Harvard University - [#2 Top End Mathematics]
2 Stanford University - [#2 Top End Mathematics]
3 University of California, Berkeley - [#2 Top End Mathematics]
5 Massachusetts Institute of Technology - [#2 Top End Mathematics]
9 University of Chicago - [#6 Top End Mathematics]
6 California Institute of Technology - [#7 Top End Mathematics]
11 Yale University - [#7 Top End Mathematics]
7 Columbia University - [#9 Top End Mathematics]
22 University of Michigan, Ann Arbor - [#9 Top End Mathematics]
32 New York University - [#9 Top End Mathematics]
-----
13 University of California, Los Angeles - [#12 Top End Mathematics]
12 Cornell University - #13 Top End Mathematics]
17 University of Wisconsin–Madison - [#14 Top End Mathematics]
38 University of Texas at Austin - [#14 Top End Mathematics]
69 Brown University - Providence, RI - [#14 Top End Mathematics]
28 University of Minnesota, Twin Cities - [#17 Top End Mathematics]
15 University of Pennsylvania - [#18 Top End Mathematics]
25 University of Illinois at Urbana-Champaign - [#18 Top End Mathematics]
30 Northwestern University - Evanston, IL - [#18 Top End Mathematics]
-----
19 Johns Hopkins University - [#21 Top End Mathematics]
31 Duke University - Durham, NC - [#21 Top End Mathematics]
37 University of Maryland, College Park - [#21 Top End Mathematics]
14 University of California, San Diego - [#24 Top End Mathematics]
16 University of Washington - [#24 Top End Mathematics]
55 Rutgers University - Piscataway, NJ - [#24 Top End Mathematics]
167 State University of New York at Stony Brook - Stony Brook, NY - [#24 Top End Mathematics]
39 University of North Carolina at Chapel Hill - [#28 Top End Mathematics]
45 Pennsylvania State University-University Park - [#28 Top End Mathematics]
67 Purdue University - West Lafayette, IN - [#28 Top End Mathematics]
93 Indiana University - Bloomington, IN - [#28 Top End Mathematics]
99 Rice University - Houston, TX - [#28 Top End Mathematics]
-----
59 Carnegie Mellon University - Pittsburgh, PA - [#33 Top End Mathematics]
62 Ohio State University - Columbus, OH - [#33 Top End Mathematics]
80 University of Utah - Salt Lake City, UT - [#33 Top End Mathematics]
9 University of California, Davis - [#36 Top End Mathematics]
104 Georgia Institute of Technology - Atlanta, GA - [#36 Top End Mathematics]
182 University of Illinois at Chicago - [#36 Top End Mathematics]
308 City University of New York City College - New York, NY - [#36 Top End Mathematics]
-----
29 Washington University in St. Louis - [#40 Top End Mathematics]
78 University of Arizona - Tucson, AZ - [#40 Top End Mathematics]
92 University of Virginia - Charlottesville, VA - [#40 Top End Mathematics]
201 Brandeis University - Waltham, MA - [#40 Top End Mathematics]
47 University of California, Irvine - #44 Top End Mathematics]
86 Michigan State University - East Lansing, MI - [#44 Top End Mathematics]
89 Texas A&M University - College Station, TX - #44 Top End Mathematics]
280 University of Notre Dame - Notre Dame, IN - [#44 Top End Mathematics]
34 University of Colorado - [#48 Top End Mathematics]
35 University of California, Santa Barbara - [#48 Top End Mathematics]
42 Vanderbilt University - Nashville, TN - [#48 Top End Mathematics]
74 Boston University - Boston, MA - [#48 Top End Mathematics]
103 Dartmouth College - Hanover, NH - [#48 Top End Mathematics]
111 North Carolina State University - Raleigh, NC - [#48 Top End Mathematics]
198 Virginia Polytechnic Institute and State University [Virginia Tech] - Blacksburg, VA - [#48 Top End Mathematics]
-----
46 University of Southern California - Los Angeles - [#55 Top End Mathematics]
116 The University of Georgia - Athens, GA - #55 Top End Mathematics]
51 University of Pittsburgh - PA - [#58 Top End Mathematics]
58 University of Florida - Gainesville, FL - [#58 Top End Mathematics]
227 Rensselaer Polytechnic Institute - Troy, NY - [#58 Top End Mathematics]
277 University of Missouri - Columbia, MO - [#58 Top End Mathematics]
281 University of Oregon - Eugene, OR - [#58 Top End Mathematics]
444 Northeastern University - Boston, MA - [#58 Top End Mathematics]
-----
132 University of Iowa - Iowa City, IA - [#55 Top End Mathematics]
94 Arizona State University - Tempe, AZ - [#64 Top End Mathematics]
136 University of Massachusetts Amherst - Worcester, MA - [#64 Top End Mathematics]
158 Iowa State University - Ames, IA - [#64 Top End Mathematics]
215 Louisiana State University - Baton Rouge, LA - [#64 Top End Mathematics]
268 University of Kansas - Lawrence, KS - [#64 Top End Mathematics]
500+ Claremont Graduate University Claremont, CA - [#64 Top End Mathematics]
-----
79 University of Rochester - Rochester, NY - #70 Top End Mathematics]
125 University of California, Riverside - Riverside, CA - [#70 Top End Mathematics]
155 Florida State University - Tallahassee, FL - [#70 Top End Mathematics]
178 University of Delaware - Newark, DE - [#70 Top End Mathematics]
193 University of Tennessee - Knoxville, TN - [#70 Top End Mathematics]
100 Emory University - Atlanta, GA - [#75 Top End Mathematics]
121 Tufts University - Medford, MA - [#75 Top End Mathematics]
126 University of California, Santa Cruz - [#75 Top End Mathematics]
270 University of Kentucky - Lexington, KY - [#75 Top End Mathematics]
326 Kansas State University - Manhattan, KS - [#75 Top End Mathematics]
345 Syracuse University - Syracuse, NY - [#75 Top End Mathematics]
347 Temple University - Philadelphia, PA - [#75 Top End Mathematics]
357 Tulane University - New Orleans, LA - [#75 Top End Mathematics]
379 University of Oklahoma - Norman, OK - [#75 Top End Mathematics]
-----
187 University of Nebraska - Lincoln, NE - [#84 Top End Mathematics]
234 State University of New York at Buffalo - [#84 Top End Mathematics]
244 The University of New Mexico - Albuquerque - [#84 Top End Mathematics]
266 University of Houston - Houston, TX - [#84 Top End Mathematics]
296 Washington State University - Pullman, WA - [#84 Top End Mathematics]
500+ SUNY-Binghamton Binghamton, NY - [#84 Top End Mathematics]
-----
87 Case Western Reserve University - Cleveland, OH - [#90 Top End Mathematics]
112 Oregon State University - Corvallis, OR - [#90 Top End Mathematics]
152 Colorado State University - Fort Collins, CO - [#90 Top End Mathematics]
170 The University of Connecticut - Storrs, CT - [#90 Top End Mathematics]
233 State University of New York at Albany - [#90 Top End Mathematics]
286 University of South Carolina - Columbia, SC - [#90 Top End Mathematics]
400 Auburn University - Auburn, AL - [#90 Top End Mathematics]
432 Lehigh University - Bethlehem, PA - [#90 Top End Mathematics]
500+ Oklahoma State University Stillwater, OK - [#90 Top End Mathematics]
500+ Rutgers, the State University of New Jersey-Newark Newark, NJ - [#90 Top End Mathematics]
-----
18 University of California, San Francisco - [Not in the Top End Mathematics]
33 Rockefeller University - [Not in the Top End Mathematics]
-----
-----
-----and for perspective
world-wide

-----
4 University of Cambridge, England - [#5 World Ranking Mathematics]
44 University of Paris 11 [Paris-Sud 11 University], France - [#6 World Ranking Mathematics]
40 University of Paris 6 [Pierre and Marie Curie University], France - [#7 World Ranking Mathematics]
10 University of Oxford, England - [#8 World Ranking Mathematics]
[example] - 5 Massachusetts Institute of Technology - [#9 World Ranking Mathematics]
-----
77 Moscow State University, Russia - [#23 World Ranking Mathematics]
115 Tel Aviv University, Ramat Aviv, Israel - [#25 World Ranking Mathematics]
[example] - 38 University of Texas at Austin - [#26 World Ranking Mathematics]
-----
24 Kyoto University, Japan - [#33 World Ranking Mathematics]
98 University of Bonn, Germany - [#34 World Ranking Mathematics]
382 University of Paris Dauphine [Paris 9], France - [#34 World Ranking Mathematics]
[example] - 19 Johns Hopkins University - (Rowland) Baltimore, MD - [#35 World Ranking Mathematics]
[example] - 6 California Institute of Technology - [#37 World Ranking Mathematics]
-----
196 University of Warwick, England - [#40 World Ranking Mathematics]
23 ETH Zurich [Swiss Federal Institute of Technology], Switzerland - [#42 World Ranking Mathematics]
27 University of Toronto, Canada - [#43 World Ranking Mathematics]
143 University of Pisa, Italy - [#44 World Ranking Mathematics]
[example] - 25 University of Illinois at Urbana-Champaign - [#45 World Ranking Mathematics]
26 Imperial College London [The Imperial College of Science, Technoloy and Medicine], England - [#46 World Ranking Mathematics]
70 Ecole Normale Superieure - Paris, France - [#47 World Ranking Mathematics]
61 University of Bristol. England - [#48 World Ranking Mathematics]
110 National University of Singapore, Kent Ridge, Singapore - [#49 World Ranking Mathematics]
142 University of Paris Diderot [Paris 7], France - [#50 World Ranking Mathematics]
-----
20 The University of Tokyo, Japan - Tied #50-75 World Ranking Mathematics]
52 University of Utrecht, Holland - [Tied #50-75 World Ranking Mathematics]
60 Australian National University, Australia - [Tied #50-75 World Ranking Mathematics]
64 Hebrew University of Jerusalem, Israel - [Tied #50-75 World Ranking Mathematics]
114 Technion-Israel Institute of Technology, Haifa, Israel - [Tied #50-75 World Ranking Mathematics]
200 Autonomous University of Madrid, Spain - [Tied #50-75 World Ranking Mathematics]
206 Ecole Polytechnique, France - [Tied #50-75 World Ranking Mathematics]
224 Peking University, Peking, China - [Tied #50-75 World Ranking Mathematics]
236 The Chinese University of Hong Kong, Hong Kong - [Tied #50-75 World Ranking Mathematics]
340 Scuola Normale Superiore - Pisa, Italy - [Tied #50-75 World Ranking Mathematics]
363 University of Bielefeld, Germany - [Tied #50-75 World Ranking Mathematics]
385 University of Rennes 1, France - [Tied #50-75 World Ranking Mathematics]
500+ Humboldt University of Berlin, Berlin, Germany - [Tied #50-75 World Ranking Mathematics]
[example] - 34 University of Colorado - Boulder, CO - [Tied #50-75 World Ranking Mathematics]
[example] - 45 Pennsylvania State University - University Park, PA - [Tied #50-75 World Ranking Mathematics]
-----
21 University College London, England - [Tied #75-100 World Ranking Mathematics]
41 University of Manchester, England - [Tied #75-100 World Ranking Mathematics]
54 University of Zurich, Switzerland - [Tied #75-100 World Ranking Mathematics]
66 McGill University, Canada - [Tied #75-100 World Ranking Mathematics]
106 Louis Pasteur University [Strasbourg I], France - [Tied #75-100 World Ranking Mathematics]
120 Tokyo Institute of Technology, Japan - [Tied #75-100 World Ranking Mathematics]
139 University of Milan, Italy - [Tied #75-100 World Ranking Mathematics]
141 University of Muenster, Germany - [Tied #75-100 World Ranking Mathematics]
147 University of Tuebingen, Germany - [Tied #75-100 World Ranking Mathematics]
168 Technical University of Denmark, Denmark - [Tied #75-100 World Ranking Mathematics]
188 University of New South Wales, Australia - [Tied #75-100 World Ranking Mathematics]
229 RWTH Aachen University, Germany - [Tied #75-100 World Ranking Mathematics]
231 Simon Fraser University, Canada - [Tied #75-100 World Ranking Mathematics]
349 The Hong Kong Polytechnic University, Hong Kong - [Tied #75-100 World Ranking Mathematics]
383 University of Provence [Aix-Marseille 1], France - [Tied #75-100 World Ranking Mathematics]
------


when i came across some ranking that were interesting, i'd make up a list...

example:

2 Stanford University
Stanford University Stanford, CA

[#4 Best Undergraduate Teaching]
[#1 Top End Physics]
[#4 Atomic and Molecular Physics/Optics and Lasers]
[#6 Solid State Physics]
[#5 Relativity/Gravitation/Cosmology]
[#6 Particle Physics/Quantum Field Theory/String Theory]
[#4 Quantum Physics]
[#1 Aerospace Engineering]
[#2 Mechanical Engineering]
[#3 Civil Engineering]
[#1 Electrical Engineering]
[#3 Geophysics and Seismology]
[#2 Top End Mathematics]
[#9 Algebra and Number Theory]
[#9 Applied Mathematics]
[#4 Geometry]
[#6 Mathematical Logic]
[#8 Topology]
[#1 Statistics]
[#1 Chemistry Top End]
[#4 Physical Chemistry]
[#8 Inorganic Chemistry]
[#3 Organic Chemistry]
[#3 Cell Biology]
[#6 World Ranking Physics]
[#4 World Ranking Mathematics]
[#4 World Ranking Chemistry]
[#2 World Ranking Engineering Techology]

so if i care about a fluid dynamics text or quantum mechanics or physical chem or transistor books or geometry texts, i know where to peek...

the lists are out there, but there's a lot of funny ones, but at least knowing roughly what the ballpark is like out there is sort of fun to peek at, minus wasting a month of gut lining making up yer list...

interesting to see how the european unis rate to US ones, and how physics or math changed say in germany after the war...
 
  • #3,287


Well take it with a grain of salt, but in my spare time a whlle i mixed up a bunch of rankings for unis just for my own fun...

anyhoo Brandeis is probably in the top 40 schools for higher math...


for people who like lists...
here we go:



201 Brandeis University - Waltham, MA
[#64 Top End Physics]
[#40 Top End Mathematics]
[#68 Chemistry Top End]

------
8 Princeton University - [#1 Top End Mathematics]
1 Harvard University - [#2 Top End Mathematics]
2 Stanford University - [#2 Top End Mathematics]
3 University of California, Berkeley - [#2 Top End Mathematics]
5 Massachusetts Institute of Technology - [#2 Top End Mathematics]
9 University of Chicago - [#6 Top End Mathematics]
6 California Institute of Technology - [#7 Top End Mathematics]
11 Yale University - [#7 Top End Mathematics]
7 Columbia University - [#9 Top End Mathematics]
22 University of Michigan, Ann Arbor - [#9 Top End Mathematics]
32 New York University - [#9 Top End Mathematics]
-----
13 University of California, Los Angeles - [#12 Top End Mathematics]
12 Cornell University - #13 Top End Mathematics]
17 University of Wisconsin–Madison - [#14 Top End Mathematics]
38 University of Texas at Austin - [#14 Top End Mathematics]
69 Brown University - Providence, RI - [#14 Top End Mathematics]
28 University of Minnesota, Twin Cities - [#17 Top End Mathematics]
15 University of Pennsylvania - [#18 Top End Mathematics]
25 University of Illinois at Urbana-Champaign - [#18 Top End Mathematics]
30 Northwestern University - Evanston, IL - [#18 Top End Mathematics]
-----
19 Johns Hopkins University - [#21 Top End Mathematics]
31 Duke University - Durham, NC - [#21 Top End Mathematics]
37 University of Maryland, College Park - [#21 Top End Mathematics]
14 University of California, San Diego - [#24 Top End Mathematics]
16 University of Washington - [#24 Top End Mathematics]
55 Rutgers University - Piscataway, NJ - [#24 Top End Mathematics]
167 State University of New York at Stony Brook - Stony Brook, NY - [#24 Top End Mathematics]
39 University of North Carolina at Chapel Hill - [#28 Top End Mathematics]
45 Pennsylvania State University-University Park - [#28 Top End Mathematics]
67 Purdue University - West Lafayette, IN - [#28 Top End Mathematics]
93 Indiana University - Bloomington, IN - [#28 Top End Mathematics]
99 Rice University - Houston, TX - [#28 Top End Mathematics]
-----
59 Carnegie Mellon University - Pittsburgh, PA - [#33 Top End Mathematics]
62 Ohio State University - Columbus, OH - [#33 Top End Mathematics]
80 University of Utah - Salt Lake City, UT - [#33 Top End Mathematics]
9 University of California, Davis - [#36 Top End Mathematics]
104 Georgia Institute of Technology - Atlanta, GA - [#36 Top End Mathematics]
182 University of Illinois at Chicago - [#36 Top End Mathematics]
308 City University of New York City College - New York, NY - [#36 Top End Mathematics]
-----
29 Washington University in St. Louis - [#40 Top End Mathematics]
78 University of Arizona - Tucson, AZ - [#40 Top End Mathematics]
92 University of Virginia - Charlottesville, VA - [#40 Top End Mathematics]
201 Brandeis University - Waltham, MA - [#40 Top End Mathematics]
47 University of California, Irvine - #44 Top End Mathematics]
86 Michigan State University - East Lansing, MI - [#44 Top End Mathematics]
89 Texas A&M University - College Station, TX - #44 Top End Mathematics]
280 University of Notre Dame - Notre Dame, IN - [#44 Top End Mathematics]
34 University of Colorado - [#48 Top End Mathematics]
35 University of California, Santa Barbara - [#48 Top End Mathematics]
42 Vanderbilt University - Nashville, TN - [#48 Top End Mathematics]
74 Boston University - Boston, MA - [#48 Top End Mathematics]
103 Dartmouth College - Hanover, NH - [#48 Top End Mathematics]
111 North Carolina State University - Raleigh, NC - [#48 Top End Mathematics]
198 Virginia Polytechnic Institute and State University [Virginia Tech] - Blacksburg, VA - [#48 Top End Mathematics]
-----
46 University of Southern California - Los Angeles - [#55 Top End Mathematics]
116 The University of Georgia - Athens, GA - #55 Top End Mathematics]
51 University of Pittsburgh - PA - [#58 Top End Mathematics]
58 University of Florida - Gainesville, FL - [#58 Top End Mathematics]
227 Rensselaer Polytechnic Institute - Troy, NY - [#58 Top End Mathematics]
277 University of Missouri - Columbia, MO - [#58 Top End Mathematics]
281 University of Oregon - Eugene, OR - [#58 Top End Mathematics]
444 Northeastern University - Boston, MA - [#58 Top End Mathematics]
-----
132 University of Iowa - Iowa City, IA - [#55 Top End Mathematics]
94 Arizona State University - Tempe, AZ - [#64 Top End Mathematics]
136 University of Massachusetts Amherst - Worcester, MA - [#64 Top End Mathematics]
158 Iowa State University - Ames, IA - [#64 Top End Mathematics]
215 Louisiana State University - Baton Rouge, LA - [#64 Top End Mathematics]
268 University of Kansas - Lawrence, KS - [#64 Top End Mathematics]
500+ Claremont Graduate University Claremont, CA - [#64 Top End Mathematics]
-----
79 University of Rochester - Rochester, NY - #70 Top End Mathematics]
125 University of California, Riverside - Riverside, CA - [#70 Top End Mathematics]
155 Florida State University - Tallahassee, FL - [#70 Top End Mathematics]
178 University of Delaware - Newark, DE - [#70 Top End Mathematics]
193 University of Tennessee - Knoxville, TN - [#70 Top End Mathematics]
100 Emory University - Atlanta, GA - [#75 Top End Mathematics]
121 Tufts University - Medford, MA - [#75 Top End Mathematics]
126 University of California, Santa Cruz - [#75 Top End Mathematics]
270 University of Kentucky - Lexington, KY - [#75 Top End Mathematics]
326 Kansas State University - Manhattan, KS - [#75 Top End Mathematics]
345 Syracuse University - Syracuse, NY - [#75 Top End Mathematics]
347 Temple University - Philadelphia, PA - [#75 Top End Mathematics]
357 Tulane University - New Orleans, LA - [#75 Top End Mathematics]
379 University of Oklahoma - Norman, OK - [#75 Top End Mathematics]
-----
187 University of Nebraska - Lincoln, NE - [#84 Top End Mathematics]
234 State University of New York at Buffalo - [#84 Top End Mathematics]
244 The University of New Mexico - Albuquerque - [#84 Top End Mathematics]
266 University of Houston - Houston, TX - [#84 Top End Mathematics]
296 Washington State University - Pullman, WA - [#84 Top End Mathematics]
500+ SUNY-Binghamton Binghamton, NY - [#84 Top End Mathematics]
-----
87 Case Western Reserve University - Cleveland, OH - [#90 Top End Mathematics]
112 Oregon State University - Corvallis, OR - [#90 Top End Mathematics]
152 Colorado State University - Fort Collins, CO - [#90 Top End Mathematics]
170 The University of Connecticut - Storrs, CT - [#90 Top End Mathematics]
233 State University of New York at Albany - [#90 Top End Mathematics]
286 University of South Carolina - Columbia, SC - [#90 Top End Mathematics]
400 Auburn University - Auburn, AL - [#90 Top End Mathematics]
432 Lehigh University - Bethlehem, PA - [#90 Top End Mathematics]
500+ Oklahoma State University Stillwater, OK - [#90 Top End Mathematics]
500+ Rutgers, the State University of New Jersey-Newark Newark, NJ - [#90 Top End Mathematics]
-----
18 University of California, San Francisco - [Not in the Top End Mathematics]
33 Rockefeller University - [Not in the Top End Mathematics]
-----
-----
-----


and for perspective
world-wide

-----
4 University of Cambridge, England - [#5 World Ranking Mathematics]
44 University of Paris 11 [Paris-Sud 11 University], France - [#6 World Ranking Mathematics]
40 University of Paris 6 [Pierre and Marie Curie University], France - [#7 World Ranking Mathematics]
10 University of Oxford, England - [#8 World Ranking Mathematics]
[example] - 5 Massachusetts Institute of Technology - [#9 World Ranking Mathematics]
-----
77 Moscow State University, Russia - [#23 World Ranking Mathematics]
115 Tel Aviv University, Ramat Aviv, Israel - [#25 World Ranking Mathematics]
[example] - 38 University of Texas at Austin - [#26 World Ranking Mathematics]
-----
24 Kyoto University, Japan - [#33 World Ranking Mathematics]
98 University of Bonn, Germany - [#34 World Ranking Mathematics]
382 University of Paris Dauphine [Paris 9], France - [#34 World Ranking Mathematics]
[example] - 19 Johns Hopkins University - (Rowland) Baltimore, MD - [#35 World Ranking Mathematics]
[example] - 6 California Institute of Technology - [#37 World Ranking Mathematics]
-----
196 University of Warwick, England - [#40 World Ranking Mathematics]
23 ETH Zurich [Swiss Federal Institute of Technology], Switzerland - [#42 World Ranking Mathematics]
27 University of Toronto, Canada - [#43 World Ranking Mathematics]
143 University of Pisa, Italy - [#44 World Ranking Mathematics]
[example] - 25 University of Illinois at Urbana-Champaign - [#45 World Ranking Mathematics]
26 Imperial College London [The Imperial College of Science, Technoloy and Medicine], England - [#46 World Ranking Mathematics]
70 Ecole Normale Superieure - Paris, France - [#47 World Ranking Mathematics]
61 University of Bristol. England - [#48 World Ranking Mathematics]
110 National University of Singapore, Kent Ridge, Singapore - [#49 World Ranking Mathematics]
142 University of Paris Diderot [Paris 7], France - [#50 World Ranking Mathematics]
-----
20 The University of Tokyo, Japan - Tied #50-75 World Ranking Mathematics]
52 University of Utrecht, Holland - [Tied #50-75 World Ranking Mathematics]
60 Australian National University, Australia - [Tied #50-75 World Ranking Mathematics]
64 Hebrew University of Jerusalem, Israel - [Tied #50-75 World Ranking Mathematics]
114 Technion-Israel Institute of Technology, Haifa, Israel - [Tied #50-75 World Ranking Mathematics]
200 Autonomous University of Madrid, Spain - [Tied #50-75 World Ranking Mathematics]
206 Ecole Polytechnique, France - [Tied #50-75 World Ranking Mathematics]
224 Peking University, Peking, China - [Tied #50-75 World Ranking Mathematics]
236 The Chinese University of Hong Kong, Hong Kong - [Tied #50-75 World Ranking Mathematics]
340 Scuola Normale Superiore - Pisa, Italy - [Tied #50-75 World Ranking Mathematics]
363 University of Bielefeld, Germany - [Tied #50-75 World Ranking Mathematics]
385 University of Rennes 1, France - [Tied #50-75 World Ranking Mathematics]
500+ Humboldt University of Berlin, Berlin, Germany - [Tied #50-75 World Ranking Mathematics]
[example] - 34 University of Colorado - Boulder, CO - [Tied #50-75 World Ranking Mathematics]
[example] - 45 Pennsylvania State University - University Park, PA - [Tied #50-75 World Ranking Mathematics]
-----
21 University College London, England - [Tied #75-100 World Ranking Mathematics]
41 University of Manchester, England - [Tied #75-100 World Ranking Mathematics]
54 University of Zurich, Switzerland - [Tied #75-100 World Ranking Mathematics]
66 McGill University, Canada - [Tied #75-100 World Ranking Mathematics]
106 Louis Pasteur University [Strasbourg I], France - [Tied #75-100 World Ranking Mathematics]
120 Tokyo Institute of Technology, Japan - [Tied #75-100 World Ranking Mathematics]
139 University of Milan, Italy - [Tied #75-100 World Ranking Mathematics]
141 University of Muenster, Germany - [Tied #75-100 World Ranking Mathematics]
147 University of Tuebingen, Germany - [Tied #75-100 World Ranking Mathematics]
168 Technical University of Denmark, Denmark - [Tied #75-100 World Ranking Mathematics]
188 University of New South Wales, Australia - [Tied #75-100 World Ranking Mathematics]
229 RWTH Aachen University, Germany - [Tied #75-100 World Ranking Mathematics]
231 Simon Fraser University, Canada - [Tied #75-100 World Ranking Mathematics]
349 The Hong Kong Polytechnic University, Hong Kong - [Tied #75-100 World Ranking Mathematics]
383 University of Provence [Aix-Marseille 1], France - [Tied #75-100 World Ranking Mathematics]
------


when i came across some ranking that were interesting, i'd make up a list...

example:

2 Stanford University
Stanford University Stanford, CA

[#4 Best Undergraduate Teaching]
[#1 Top End Physics]
[#4 Atomic and Molecular Physics/Optics and Lasers]
[#6 Solid State Physics]
[#5 Relativity/Gravitation/Cosmology]
[#6 Particle Physics/Quantum Field Theory/String Theory]
[#4 Quantum Physics]
[#1 Aerospace Engineering]
[#2 Mechanical Engineering]
[#3 Civil Engineering]
[#1 Electrical Engineering]
[#3 Geophysics and Seismology]
[#2 Top End Mathematics]
[#9 Algebra and Number Theory]
[#9 Applied Mathematics]
[#4 Geometry]
[#6 Mathematical Logic]
[#8 Topology]
[#1 Statistics]
[#1 Chemistry Top End]
[#4 Physical Chemistry]
[#8 Inorganic Chemistry]
[#3 Organic Chemistry]
[#3 Cell Biology]
[#6 World Ranking Physics]
[#4 World Ranking Mathematics]
[#4 World Ranking Chemistry]
[#2 World Ranking Engineering Techology]

so if i care about a fluid dynamics text or quantum mechanics or physical chem or transistor books or geometry texts, i know where to peek...

the lists are out there, but there's a lot of funny ones, but at least knowing roughly what the ballpark is like out there is sort of fun to peek at, minus wasting a month of gut lining making up yer list...

interesting to see how the european unis rate to US ones, and how physics or math changed say in germany after the war...
 
  • #3,288


as for textbooks, recall that Mike Spivak was at Brandeis when he wrote both his calculus book and his differential geometry series. So those books which are considered the gold standard in both subjects were written specifically for courses at Brandeis. When I was there I also attended some undergraduate classes in algebra where the lecturer was adapting the famous books by Bourbaki to his class.for some current textbooks, consult individual instructor's webpages, e.g.

http://people.brandeis.edu/~cherveny/

http://people.brandeis.edu/~hsultan/

http://people.brandeis.edu/~jbellaic/teaching.html

http://people.brandeis.edu/~bernardi/index.php?page=teaching

http://people.brandeis.edu/~kleinboc/
 
Last edited:
  • #3,289


What was Mike Spivak's inspiration for his calculus and diff geometry books? I am always curious what they *used* when they were in school, and sometimes the list of what they thought were great books, or not-so great books... when they were starting out...

I think what i remember most about Spivak's book was i saw it offered once, by one teacher in one class for calculus at the local uni, and didnt see it before or after... I didn't know which book it was other than it was plain looking and 'furry' and i was really impressed with the back that had tons of comments about dozens and dozens of texts, and i thought, wow 3 sentences about Hardy's Pure Mathematics... or a line or two about Courant...

always liked textbooks, in first year that would slide in some recommended books that way...
 
  • #3,290


i want to be a mathematician, but i don't hve the natural talent for it..


we need mathematicans today to solve the great underlying mysteries of math today.
 

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