0
votes
2answers
104 views

General question about undergrad math classes? [closed]

I'm currently in Real Analysis 2, and while I'm doing pretty well, it's just so much time and effort to finish all the problem sets and do well on the exams. I only have a few math classes left for ...
1
vote
1answer
27 views

Is $g$ increasing?

Suppose $f:[a,b]\rightarrow\mathbb{R}$ and define $g:[a,b]\rightarrow\mathbb{R}$ as follows $$ g(x)=\sup\{f(t):a\leq t\leq x\}, $$ with $x\in[a,b]$. Someone told me that $g$ is an increasing ...
0
votes
0answers
83 views

Multivariable calculus and real analysis in one semester. What is the best way to study for such course?

I am in my first year of EECS and planning on taking a lot of maths classes. I have already taken single variable calculus and linear algebra and did well in them and decided to take multivariable ...
4
votes
0answers
65 views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
4
votes
3answers
974 views

I am failing at Analysis again. [closed]

I am stuck at this very hard course again. I don't want to put blames but if you were to ask me, what is going wrong I would say: The professor teaches too bluntly The book is too hard to ...
3
votes
0answers
76 views

My first simple direct proof (very simple theorem on real numbers). Please mark/grade.

What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Let $I = [a,b]$ be a non-empty closed ...
0
votes
1answer
386 views

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level?

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level? Will these prerequisites help me with these two coursea at the graduate level? or do I ...
2
votes
6answers
434 views

Need advice on whether I should take Algebra 2 next semester

I am an undergraduate primarily interested in pure mathematics, but recently ODE and Linear Algebra have caught my attention. As I study more applied maths, I have less time for pure math. My ...
3
votes
2answers
132 views

Real Exponentiation (help with an exercise)

Hi everyone I have serious problems with this exercise. I would appreciate any help. Thanks. (I can use freely any fact regard to real exponentiation when the exponent is a rational number, other ...
1
vote
1answer
212 views

Which topics of real-analysis should be studied if you have already done calculus

Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
3
votes
1answer
331 views

Taking an exam in math analysis course.

So I'm taking my first midterm exam in math analysis soon and I'm confused on how to study for it. I mean in calculus one would be able to just go into the book and take derivatives and integrals ...
3
votes
1answer
380 views

Goldberg against Rudin against Pugh. Which real analysis book should I buy? [closed]

I am trying to decided which real analysis text book I should buy. I have the following in mind- 1)Walter Rudin's "Principles of Mathematical Analysis" 2)Charles Pugh's "Real Mathematical Analysis" ...
5
votes
2answers
1k views

Rudin against Pugh for Textbook for First Course in Real Analysis

So as I have said before in a previous question, I am taking a first course in Mathematical Analysis, and I'm quite excited. I just found out though that unlike the other professors at my university, ...
5
votes
2answers
363 views

Advice about taking mathematical analysis class

I appologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really ...
3
votes
3answers
418 views

Should analysis be studied minus point set topology

I have noticed that certain texts like Terry Tao's Analysis I, Bartle and Sherbert's Real analysis as well as Michael Spivak do not use the language of topology in their exposition. A text like ...
0
votes
3answers
46 views

Example of no inclusion in set of closures

Let $(X,d)$ be a metric space and $A_j \subseteq X$ for $j = 1,2,...$ . Let $B = \bigcup_{j=1}^\infty A_j$. Find an example for which $\bigcup_{j=1}^\infty \bar{A_j} \neq \bar{B}$. Also, in general ...
6
votes
2answers
413 views

Recommendations for real analysis

I have completed two courses in real analysis that covered up to chapter 9 in Rudin's Principle of Mathematical Analysis (and one on complex analysis). So if I am interested in continuing on in ...