Self-study Alegbra, PHysics and trigonometry books?

[christian0710]

Hi awesome people at physicsforum,
I’m planning on doing some self-study in physics and math and I’d really appreciate some advice based on my skill -level and what I want to achieve, which I’ll describe for you. I’ve considered some books to buy further down, and would deeply appreciate some more suggestions.


What Am I looking for?
I want to gain a basic understanding in Classical mechanics and in Electromagnetism at a 1st year university level. I’m not planning on going into deep physics – so far -, I just want a basic understanding of how it works in theory and in practical situations. Also I want to strengthen my algebra, trigonometry and mathematical thinking so I can become better at setting up mathematical equations from word problems or physics scenarios.

My level of skill
I did high school Physics (Enough to begin a University study in physics), some years ago, but I’m getting rusty, I also just finished a calculus course at university, but my algebra and trigonometry is also rusty.


My Challenges and difficulties
I often have difficulties when it comes to algebra and geometry and would like to strengthen my understanding of geometry (visually and mathematically)and the rules that apply to it. Also
Also I find it difficult to understand


The BOOKS I have considered and suggestions I’d like to hear from you:

Introductory physics books which I’ve considered buying.
So Far I’ve considered buying University physics by Young and Freedman: I hear it’s easy to follow, and convers a 1st year curriculum, however people also say It’s very wordy and that some of the derivations are hard to follow . What do you say? Also, would you recommend I buy some extra physics study guide books or formulae tables as a supplement to this book? I’ve considered “Physics – A student companion”


Thinking mathematically when solving problems.
I’d love to have a self-study book teaching you how to setup mathematical expressions from word problems and in general. Being able to set up mathematical equations from experiments, mathematical relationships, or from different variables is something I’d love to be better at, and I’m willing to practice, and I think this is critical in physics. Any suggestions?


Algebra and Geometry skills and practice.
In order to practice my algebra skills I bought this book
College Algebra Demystefied 2Ed, I’d love to have more suggestions perhaps to some more advanced algebra, and a book giving me a good insight with respect to geometry, trig functions etc.

 

[jedishrfu]

There are multiple routes:

1) PF has lists of materials on these subjects under the Forums pulldown under "Science Education" selection.

2) the book Physics for the IB Diploma by Tsokos covers First Year college physics

https://www.amazon.com/dp/0521138213/?tag=pfamazon01-20

3) Khans Academy website (www.khansacademy.org[/URL]) has many videos on math (Algebra, Geometry, Trignometry and Calculus) and on Physics

4) MathIsPower4U ([url]http://mathispower4u.yolasite.com/[/url]) has many math videos covering the same range of math including Differentil Eqns, Linear Algebra and Advanced Calculus with some videos on Vector Calculus.

 

[micromass]

Algebra and Geometry skills and practice.
In order to practice my algebra skills I bought this book
College Algebra Demystefied 2Ed, I’d love to have more suggestions perhaps to some more advanced algebra, and a book giving me a good insight with respect to geometry, trig functions etc.

I highly recommend the book "Basic Mathematics" by Lang. It really contains all the mathematics you should know from high school to be successful in calculus, math and physics. It doesn't contain extra unnecessary fluff which eventually becomes trivial once you know calculus.

I also recommend the two books "Algebra" and "Trigonometry" by Gelfand. Gelfand (and Lang too by the way) is a top mathematician, a really big name in the field. He wrote a series of high school books and they are simply brilliant. It is filled with motivation and understanding why things are true

 

[verty]

https://www.amazon.com/dp/1576855104/?tag=pfamazon01-20

I think this is better than any word problem book because this is the skill one needs. Once you can see through the words, you'll easily recognize the type of problem that is being presented to you. Probably you'll want to do 2 or so passages each day until it becomes very easy.

https://www.amazon.com/dp/0201603225/?tag=pfamazon01-20

I don't know what to suggest for math review. There are books with insight but perhaps that should wait until you are done with College Algebra Demystified because the books with insight are more abstract and more demanding. (I see Micromass has responded so I'll defer to him in this regard.)

 

[verty]

https://www.amazon.com/dp/1576855104/?tag=pfamazon01-20

I think this is better than any word problem book because this is the skill one needs...

I want to say something more about this, the passages and questions look very good in this book but it gives some test-taking strategies that I think are a little like cheating:

1) It mentions underlining important words or concepts. This is not a good idea, you want to read the passage with a critical eye and understand what it is saying but not with these type of aids, one doesn't want to always have to do this.

2) It mentions reading the questions first. This is not a good idea because the point is not to scan for answers but to read critically for understanding. The questions are giving you information that you want to be extracting from the passage without that head start.

3) It recommends eliminating multiple-choice answers that you know to be false. The point is to refer back to the passage to find the answer, not to find the answer by elimination. All of these are meant to help with test-taking but I think they just short-circuit the learning.

I stand by my recommendation though, I think this is an excellent way to get better at word problems in general.

 

[christian0710]

I highly recommend the book "Basic Mathematics" by Lang. It really contains all the mathematics you should know from high school to be successful in calculus, math and physics. It doesn't contain extra unnecessary fluff which eventually becomes trivial once you know calculus.

I also recommend the two books "Algebra" and "Trigonometry" by Gelfand. Gelfand (and Lang too by the way) is a top mathematician, a really big name in the field. He wrote a series of high school books and they are simply brilliant. It is filled with motivation and understanding why things are true

I will for sure buy Basic mathematics by Lang to practice Algebra – Great Recommendation! Would You recommend I buy Algebra By gelfand in addition to Basic mathematics or does Lang cover most of the material by Gelfand?

I’m a little unsure with respect to Trigonometry by Gelfand based on the amazon.com reviews mentioning that it’s not recommended for self-study and a quote “author couldn't have picked a more perplexing way to explain this subject. Yes it's filled with problems, but what good are the problems if you don't have the correct answer nor do you have an explanation on how to solve them”
I don’t know how trustworthy the reviews are, but here is an idea of what I’m looking for in a trig book- perhaps Gelfand meets some of the criteria?

1) Explains the basic concepts well so you are not in doubt of what point is being made- not having to guess what is meant through my own deductive reasoning in chapters covering theory (I’d rather save the deductive reasoning for problems in the end of chapters) – So clear and concise instructions, in plain English, however mixing that with interesting and motivating examples or relationships would be an ideal book.
2) Visual images – I find it very important in trigonometry book.
3) Problems with answers so you are sure you did it right.


So far my algrbra need is Satesfied :D

 

[christian0710]

There are multiple routes: (1,2,3,4,5)

Thank you for the aadditional material i can use as a substitute. I do prefere to read books and leave my computer off, i don't know why - I just seems to think more clearly when working with a book and paper, however, I really think this will be very useful if there is something I can't find in my books so thanks again!

501 Critical Reading Questions

Interesting, so this has nothing with algebra to do? Is it for improving reading comprehension? I do find that I'm a very slow reader, but that's because i read so much scientific stuff, so i have to digest and absorbe it, and I never really sat down and practiced speed reading because I find there is so much confusing information on speed reading such as people claiming you can read thousands of words if you stop subvocalizing, but this book sounds interesting.

 

[micromass]

I will for sure buy Basic mathematics by Lang to practice Algebra – Great Recommendation! Would You recommend I buy Algebra By gelfand in addition to Basic mathematics or does Lang cover most of the material by Gelfand?

I’m a little unsure with respect to Trigonometry by Gelfand based on the amazon.com reviews mentioning that it’s not recommended for self-study and a quote “author couldn't have picked a more perplexing way to explain this subject. Yes it's filled with problems, but what good are the problems if you don't have the correct answer nor do you have an explanation on how to solve them”
I don’t know how trustworthy the reviews are, but here is an idea of what I’m looking for in a trig book- perhaps Gelfand meets some of the criteria?

1) Explains the basic concepts well so you are not in doubt of what point is being made- not having to guess what is meant through my own deductive reasoning in chapters covering theory (I’d rather save the deductive reasoning for problems in the end of chapters) – So clear and concise instructions, in plain English, however mixing that with interesting and motivating examples or relationships would be an ideal book.
2) Visual images – I find it very important in trigonometry book.
3) Problems with answers so you are sure you did it right.


So far my algrbra need is Satesfied :D

Lang really has everything you need to know. I don't think there is a need to get both Lang and Gelfand.

That said, I don't really agree with the review on amazon. However, it is certainly true that Gelfand is not for the typical HS student (who is generally not interested in mathematics). The book really does contain a lot of beautiful insights that are hard to find on other books. It's not the most easy book though.

 

[christian0710]

Lang really has everything you need to know. I don't think there is a need to get both Lang and Gelfand.

That said, I don't really agree with the review on amazon. However, it is certainly true that Gelfand is not for the typical HS student (who is generally not interested in mathematics). The book really does contain a lot of beautiful insights that are hard to find on other books. It's not the most easy book though.

When you say "not the most easy book" then what does it imply? Is it not easy to follow because it's not structured well, or because there are many things you have to derive on your own through your own algebraic intuition/knowledge? Are the conclusions and explanations clear and easy to understand for a nonmathematician (meaning without the abstract philosophical and mathemematical jargon, more like in plain english) such as a chemistry/biology scientist?

 

[micromass]

When you say "not the most easy book" then what does it imply? Is it not easy to follow because it's not structured well, or because there are many things you have to derive on your own through your own algebraic intuition/knowledge? Are the conclusions and explanations clear and easy to understand for a nonmathematician (meaning without the abstract philosophical and mathemematical jargon, more like in plain english) such as a chemistry/biology scientist?

It's in the sense that you actually need to put some thoughts in. It's not like usual high school books where everything is spelled out for you and you can just do it as bed time reading. It also has no cartoons and all the other irrelevant things you find in high school books. It's a true mathematics book. It is on the level of a high school student, but the student needs to invest some brain power in it.

 

[christian0710]

It's in the sense that you actually need to put some thoughts in. It's not like usual high school books where everything is spelled out for you and you can just do it as bed time reading. It also has no cartoons and all the other irrelevant things you find in high school books. It's a true mathematics book. It is on the level of a high school student, but the student needs to invest some brain power in it.

Just a last question with respect to Gelfield, and i'll be forever grateful :D
which aspects of the book is it that requires much brain power? Is it because many mathematical steps are skipped? or lack of figures? I guess I'm trying to fit the book into one of two boxes: The book where concepts are so clearly spelled out that you see the relationship and understand the point without a doubt and still teaches you to become good at the subject. vs, the type of books where so many mathematical steps and figures are skipped that seeing the relationship requires a deep mathematical understanding - However I do think I'd learn much from trigonometry by understanding why the relationships work, and being able to visualize it so i'd need some visual figures. Where in my two generalize boxes do you think Gelfands fits?

 

[micromass]

Just a last question with respect to Gelfield, and i'll be forever grateful :D
which aspects of the book is it that requires much brain power? Is it because many mathematical steps are skipped? or lack of figures? I guess I'm trying to fit the book into one of two boxes: The book where concepts are so clearly spelled out that you see the relationship and understand the point without a doubt and still teaches you to become good at the subject. vs, the type of books where so many mathematical steps and figures are skipped that seeing the relationship requires a deep mathematical understanding - However I do think I'd learn much from trigonometry by understanding why the relationships work, and being able to visualize it so i'd need some visual figures. Where in my two generalize boxes do you think Gelfands fits?

It's really difficult for me to answer that for you because all people are different. For me personally, I don't think many steps are skipped and I think the concepts are made clear. But I have been doing advanced math for years so my view on math textbooks is likely skewed. What is clear for me, might not be immediately clear for others.

I can certainly say that the book contains a lot of visual figures, and the book certainly does explain the "why". But is it written in a language that is suitable for you? I don't know. The best I can say is to check it out. Parts of the first two chapters are freely available online: http://books.google.be/books?id=ZCY...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Why not read 3 or 4 pages and see how you like it?

 

[verty]

[Regarding the 501 questions book,] so this has nothing with algebra to do? Is it for improving reading comprehension? I do find that I'm a very slow reader, but that's because i read so much scientific stuff, so i have to digest and absorbe it, and I never really sat down and practiced speed reading because I find there is so much confusing information on speed reading such as people claiming you can read thousands of words if you stop subvocalizing, but this book sounds interesting.

Speed reading is something very different, it is a quack theory that skeptics will tell you doesn't work. The maximum speed that one can process audible speech is about 1.3x to 1.5x normal speed and the same part of the brain is involved in processing what we read. It just isn't true that one can learn to read 10x faster.

You are correct that this book doesn't deal with algebra, the reason is that people who struggle with word problems usually do well enough when they are given the formulas directly. Most of them will say, they don't know how to get the formulas from the word description. But actually this is very easy, the words tell you everything you need to know, all the information is there, it just needs to be written down in an algebraic form.

Anyway, that is my recommendation, I think it'll help and it's up to you, it is a very cheap book after all.

 

[verty]

When you say "not the most easy book" then what does it imply?

My definition for when a book is difficult is based on three criteria. The first is how accessible the content is. Can one get a basic understanding pretty quickly after reading a section, even if this means not having detailed knowledge or not having any practical skill. But can one at least get some kind of skeletal knowledge straight away? Some books are so terse that one can hardly understand anything on a first reading. An example topic is the Heine-Borel theorem, the first time one sees that proof it is a real mindbender. A book that just gives that proof in 3 lines or so and moves on is making it very hard to get a skeletal understanding, I think.

My second criterion is how much is left to the exercises. Could one do all the exercises in a reasonable time and with reasonable effort? Some books leave too much new knowledge in the exercises, an example I can think of is "A First Course in Probability" by Sheldon Ross. It's a great book I think but many exercises go quite far beyond the material in the chapters. Also, exercises that need a spreadsheet to do are not marked and they look just the same, and some probably need math software to complete. I would class that as a difficult book.

Spivak on the other hand has exercises that are difficult but don't really have new knowledge, they just test what knowledge one has gained in the chapter very thoroughly, so I appreciate it for that reason. One thing I didn't like so much is that the solutions (at least in the first edition) didn't seem to really explain the questions at all. If a particular question was difficult, one would probably need to move on, which isn't that big of a deal but it's pushing up against the "reasonable effort" clause.

My third criterion is completeness. Is the book complete in the sense that what is covered in the exercises can be found in the chapter itself? One should be able, when faced with a difficult question, to find a hint or something closely related to it somewhere in the chapter. The exercises should test what the chapter has explained, and they can develop the content further, but it should be a relevant extension.

But sometimes you get problems that don't seem to relate to the chapter in the sense that the answer or the method can't be found there. An example is from the book "Linear Algebra Done Right" by Sheldon Axler. Chapter 2, exercise 3, this is so early in the book that you really aren't expecting it, here's the question:

Suppose $(v_1, v_2, ..., v_n)$ (a list of vectors) is independent in $V$ and $w \in V$. Prove that if $(v_1 + w, ..., v_n + w)$ is linearly dependent, then $w \in span(v_1, v_2, ..., v_n)$.

This is way too early in the book for something this obtuse. It's not a big deal, one can move on without loss but it should probably have been marked with a * or something. If one can't refer to the chapter to get help with a question, it's beyond reasonable effort. I mean, one shouldn't have to go to outside sources to unstick oneself.

I have put this here because we seem to be sort of stuck on this issue of what is a difficult book or what isn't a difficult book, so hopefully this helps matters.

 

[micromass]

This is way too early in the book for something this obtuse. It's not a big deal, one can move on without loss but it should probably have been marked with a * or something. If one can't refer to the chapter to get help with a question, it's beyond reasonable effort. I mean, one shouldn't have to go to outside sources to unstick oneself.

But Axler is not supposed to be a first book on the subject, I think. I don't think the book is that difficult if you have heard about vector spaces before in another course.

But ok, I agree with your general classification.

 

[christian0710]

I like and agree with Verty's definition of a difficult book, It explains exactly what I don't want and What I want in a book.

I think I will give Gelfands Trig book a try this summer and hope his exercises are good and not too difficult to do- Thank you a lot for the recommendation :)

With respect to a physics book, Is Young and freeman University physics the way to go? Would there be a great practical book giving a better intuition for how the theory works in the real world? Perhaps applications of physics?

 

[verty]

With respect to a physics book, Is Young and freeman University physics the way to go? Would there be a great practical book giving a better intuition for how the theory works in the real world? Perhaps applications of physics?

If anything, UP (I'll call it that) borders on being too easy, it reads like it was written for high school students who know calculus. What can I say, it's a book for learning. If you want to learn physics, this book is very good. For example, in a home schooling situation, I can't think of a better book. Some people though might think it is too well explained. Sometimes it is nice to have a challenge, to really have to think about what something means. When it is all explained, one tends to forget because it all seems obvious.

Concerning intuition, intuition is what you rely on when you don't know the theory. This teaches the theory so well that you won't need to rely on intuition, you'll know how to find the answers.

 

[christian0710]

If anything, UP (I'll call it that) borders on being too easy, it reads like it was written for high school students who know calculus. What can I say, it's a book for learning. If you want to learn physics, this book is very good. For example, in a home schooling situation, I can't think of a better book. Some people though might think it is too well explained. Sometimes it is nice to have a challenge, to really have to think about what something means. When it is all explained, one tends to forget because it all seems obvious.

Concerning intuition, intuition is what you rely on when you don't know the theory. This teaches the theory so well that you won't need to rely on intuition, you'll know how to find the answers.

From your description it sounds exactly like the type of physics book I'm looking for - Thank you for setting time aside for the help!

Thank you everyone for your help - I relly appreciate your time.

So far i bought the following books

Basic mathematics by Lang
University physics
College algebra Demystefied (already begun reading it - It's great for algebra review)
Calulus - physical Applications (think that was the name)
Forgotten calculus.

 

[verty]

From your description it sounds exactly like the type of physics book I'm looking for - Thank you for setting time aside for the help!

Thank you everyone for your help - I relly appreciate your time.

So far i bought the following books

Basic mathematics by Lang
University physics
College algebra Demystefied (already begun reading it - It's great for algebra review)
Calulus - physical Applications (think that was the name)
Forgotten calculus.

I'm sure we all wish you the very best of luck with your learning. I'll just mention that this is a good order for the math books: Demystified, Lang, Kline. Another option is to use Lang and Demystified in parallel, so you see many angles of each topic. But Kline you should leave till last because it'll be easier to learn and remember that way. And the physics, there is a ton of stuff in that book, one option is to choose topics you are interested in and learn all about them. Another option is to break the book up into parts and try to learn parts at a time. But there is far too much to just start at the start, read till the end then stop, I think it needs to be broken up somehow.

Ok, best of luck.

 

[christian0710]

I'm sure we all wish you the very best of luck with your learning. I'll just mention that this is a good order for the math books: Demystified, Lang, Kline. Another option is to use Lang and Demystified in parallel, so you see many angles of each topic. But Kline you should leave till last because it'll be easier to learn and remember that way. And the physics, there is a ton of stuff in that book, one option is to choose topics you are interested in and learn all about them. Another option is to break the book up into parts and try to learn parts at a time. But there is far too much to just start at the start, read till the end then stop, I think it needs to be broken up somehow.

Ok, best of luck.

Thnak you for your kind words. That's exactly the order i was planning on :)
I like your advice about breaking it up into subjects. I'm physics I'm actually only interested in light and electricity and then understanding the SI units, how they are defined and how other units are derived from the SI Units. I really want to get the iintuition for what Units like Newton, Joule, and current are defined and how they came about.