What should I expect from these advanced math courses?

[erraticimpulse]

I'm taking Modern Algebra 1, Real Analysis 1, and Number Systems next semester. Could someone give me an idea what to expect from these courses and maybe the workload?

 

[cronxeh]

in san ity

Edit: but seriously. Real analysis is synonymous with word 'rigorous' and both Real Analysis and Modern Algebra are considered to be graduate courses (sometimes seniors take them).

 

[shmoe]

These can vary somewhat in difficulty and content from university to university. Could you please provide some additional information such as course descriptions and the recomended textbooks if you know them?

 

[erraticimpulse]

MATH 330
NUMBER SYSTEMS
Careful discussion of the real numbers, the rational numbers and the integers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs. Prerequisites: MATH 222 with a grade of C or better.
every sem.

MATH 401
MODERN ALGEBRA I
Groups, rings, integral domains, fields. Prerequisites: MATH 304 and 330 with grades of C or better, or consent of department.
fall only

MATH 478
REAL ANALYSIS I
Geometry and topology of Rn, functions and limits, calculus of functions on Rn and higher dimensional spaces. Prerequisites: MATH 304, 323 and 330 with grades of C or better, or consent of department.
fall only

 

[Eratosthenes]

I have taken a few courses that cover some of the topics you are covering in Number Systems. It doesn't look that difficult but it requires time and effort like any other Mathematics course. You will get stuck sometimes and it will take work to understand certain concepts and ideas sometimes.


You could also try
1. Asking a professor - I am also taking courses like Modern Algebra and Real Analysis I next semester as well as 2 other senior level math courses. So I like you am wondering about the difficulty so I will probably ask a professor sometime during the summer.

2. Start studying ahead - Get a jump start by reading the material in the books the courses use and maybe finding a copy of an older syllabus for the course online and using that as a guide. I plan to do this also since I will be taking 4 mathematics courses.

3. Find out who is teaching - Most professors are very good but sometimes there are some who do not teach well, or maybe they teach well but there exams do not reflect what was taught in class. Find out who your teachers will be and be ready to study extra hard if needed.


On a side note, I had a friend who took four senior level/grad level type mathematics courses in one semester at a University that is known for it's good mathematics department. When I asked him about it he said it can be very stressful at times. Many consider him to be a math genius though so he might be an exception.


Also about Modern Algebra, I know absolutely nothing about it but a friend of mine who is fairly intelligent(he has a phd in chemistry) chose not to study math because he struggled so much in Modern Algebra. He could not understand the concepts of modern algebra and failed some "qualifying exam" he had to take to get into the mathematics program. It was his dream to become a mathematician and because of modern algebra he did not. He always tells me the story every time anything about math comes up heh. But yea maybe he had bad teacher and a difficult to read book or something, so you never know. I think a lot of it depends on your teacher and on what book you are reading. Some books suck and some are just excellent.

 

[gravenewworld]

Real Analysis aka advance calculus basically always sucks, no matter where you take it. I think 99.9% of math majors always hate and find real analysis hard.

Modern Algebra aka abstract algebra is one of my favorite courses. Group and field theory are pretty interesting and really neat.

Number systems- as for this course I don't know. I am taking a math logic course now and have covered a lot of the topics you listed. Recursive functions ,recursive sets, and recursive relations are a pain in the ass. I hated learning that stuff, its really hard. It depends on how indepth you go with it though. Proof by induction is easy once you get the hang of it. Learning about countable and uncountable sets and different sizes of infinity is interesting.

 

[erraticimpulse]

Yeah, I've heard about a lot of neat things you can do with modern algebra. Stuff with group theory and such. I've taken a Discrete Math course which seems to be an intro to math theory course. Number Systems seems to be a more indepth approach to theory from what I've gathered. But I've only heard two things about Real Analysis: rigorous and hard.

 

[MathStudent]

The math 330 course "number systems" sounds very much like an intro to upper devision math class. I think you'll find it enlightening. ( but now that I read your next post ) I see you've taken a discrete math course, which like you said, seems to cover much of the same material, so you might find it easy. In fact, you should check with a professor or counselor to see if you even need that course. If they end up being so similar then you might just want to make use of the time and take a different course.

PS: It would help if you included the textbooks, and also the names of the pre-reqs instead of the course numbers

 

[erraticimpulse]

I don't have any clue what textbooks are going to be used. I just copied the course descriptions from the website, I didn't realize that it listed course numbers instead of names.

Number systems requires MATH222 (Calculus 2).
Modern Algebra requires MATH304 (Linear Algebra) and MATH330 (Number Systems).
Real Analysis requires MATH304 (Linear Algebra) MATH323 (Calculus 3) and MATH330 (Number Systems).

 

[shmoe]

The Number Systems course looks like a bridge between the levels of rigor required in the usual calculus courses and the more 'serious' advanced classes. Have you checked that it's ok to take the Number Systems at the same time as Analysis and Algebra rather than before? If you're at the point where you can handle what will be required from the Algebra and Analysis courses, it looks like the Number Systems class will be cake.

 

[erraticimpulse]

The Number Systems course looks like a bridge between the levels of rigor required in the usual calculus courses and the more 'serious' advanced classes. Have you checked that it's ok to take the Number Systems at the same time as Analysis and Algebra rather than before? If you're at the point where you can handle what will be required from the Algebra and Analysis courses, it looks like the Number Systems class will be cake.

Is there a whole lotta difference between the discrete math I took and the number systems course offered?

DISCRETE MATHEMATICS
Sets, functions, mathematical induction, relations, partially ordered sets, combinatorics including permutations, the pigeonhole principle, binomial and multinomial coefficients, recurrence relations, generating functions, the principle of inclusion-exclusion. Graph theory, including paths and connectedness, minimum length paths, Eulerian and Hamiltonian graphs, graph isomorphisms, trees, planar and nonplanar graphs.

4 Class Hours; Prerequisite: Calculus II.

MATH 330
NUMBER SYSTEMS
Careful discussion of the real numbers, the rational numbers and the integers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs. Prerequisites: Calculus II with a grade of C or better.
every sem.

 

[MathStudent]

They look like the same class. (it looks like the discrete course actually teaches more than the number systems)

 

[semidevil]

it's going to be hard...all proof based classes...


good luck

 

[erraticimpulse]

Just in case anyone is wondering, discrete and number systems are only similar in regards to looking at a system of numbers and writing proofs. Discrete focuses on integers while Number Systems looks at the real number system.

So I really have to take number systems before I can take a course that requires it. Discrete is good but not enough. I've decided to just take Number Systems this summer as an independent study, and in doing so I can sidestep a lot of trouble (and potential academic suicide).

 

[cronxeh]

yes.. its like comparing calculus2 with real analysis. the material may be similar, but the difficulty level is very different. you should take number systems before you start real analysis and modern algebra - that would be my advice. good luck.

 

[MathStudent]

good to know

 

[mathwonk]

two serious amth classes is aplenty for almost anyone. e.g. the analysis anmd algebra.

however from the looks of the other cousre it may be a proofs cousre designed to help you with the tioher two, and could go well with one of them say. if you have not ahd proofs though, taking it and both of them is probbaly too much.

 

[erraticimpulse]

Another Question

I have a similar question, again. I know for certain that I'm taking Number Systems this summer which is a prerequisite for both Modern Algebra 1 and Real Analysis 1. I've taken the whole calculus sequence, discrete math, linear algebra, and ordinary differential equations, and I've managed to get A's/A-'s. Do you think that I would be able to take both Modern Algebra 1 and Real Analysis 1 at the same time, with other courses, and get grades in the A range?

NOTE: This question is more directed at those who have already taken Modern Algebra and Real Analysis, but other comments are welcome.

 

[mathwonk]

1) don't take advice from anyone else, make your own decisions.
2) you are going to get your **** kicked.

 

[gnome]

1) don't take advice from anyone else, make your own decisions.
2) you are going to get your **** kicked.

That's encouraging. :rofl:

 

[erraticimpulse]

1) don't take advice from anyone else, make your own decisions.

I don't think you understand that this is an academic and career guidance subforum. I'm asking for help and checking out my options. I am not obligated to follow through with any that's offered to me, but they do help me construct an informed decision.

2) you are going to get your **** kicked.

Try to be more objective. I've taken discrete math and linear algebra, which are both inherently proof-based classes, and I plan on taking number systems this summer which is entirely about proofs. From what I've gathered from professors and peers it seems that Modern Algebra and Real Analysis are both rigorous proof-based classes. With this in mind, why would it be a bad idea?

 

[Eratosthenes]

I am taking those 2 classes and 2 more proof based math classes on the same level as those next semester. I asked a prof about it he said it could be done and he said sure there are people who do it all the time.


I wouldn't worry about.

Just remember it is all math. You will get stuck, for hours, for days maybe, and you will be doing math every single day. If you don't have a problem doing math everyday then I think you will do great.

 

[stunner5000pt]

for real analysis course you have to
1) memorize the definition (not hard)
2) remember the theorem and be able to apply them (hard part)

I took an intro to real analysis course and got my behind whooped mainly because i wasnt totally prepared for what was hitting me and i never got fully up to speed. I am up to speed now (too late!)
best thing is to read your text , do all the proofs which are listed as exercises and understand what the hell you're doing! Certian theorems in Real Analysis are fundamental and they get used over and over so you neeed to have a firm grasp of them.
I guess your final chapter may be Infinite series which is supposed to be easy if you've understood the course till then.

 

[bor0000]

hey, i asked a similar question. that is i have a similar background(now taking linear algebra and vector calc). but next year wanted to take 5 rigorous math courses! i thought analysis1 and 'modern algebra', or in our school called algebra3, would be easy. for a math major one should usually take 3 math courses per semester... and since I am just starting to be a math major, i have a lot of catching up, that's why the 5 courses. but right now i don't know what to do, i m comletely unmotivated, and i have finals in a week, and the weather is so nice outside, don't feel like studying.

 

[bor0000]

p.s. i heard that linear algebra(proof-based) is equal in difficulty to real analysis1&2. And modern algebra is equal in difficulty to analysis3, that is where they do analysis of several variables.