I Post your favorite real analysis problem

AI Thread Summary
The discussion centers on sharing favorite real analysis problems, emphasizing the desire for challenging problems without solutions. Participants clarify that "real analysis" refers to topics like measure theory and functions, distinguishing it from complex analysis, which focuses on smoother functions. There is a consensus on the importance of real analysis as foundational for further mathematical studies, including topology and complex analysis. Resources such as Cambridge past exam papers and problem sheets are suggested for finding quality problems. Overall, the thread seeks to compile engaging real analysis problems for collaborative solving.
docnet
Messages
796
Reaction score
488
TL;DR Summary
I'm looking for good real analysis problems to hone my math skills. I didn't take a proper real analysis course during my BA, and skipped ahead to complex analysis and topology. And I felt that I didn't learn that much because my real analysis knowledge was shaky. And I figure it's time to catch up on what I'm lacking.
I figure one can dig around for plenty of quality problems online, but I'm hoping to skip right to the good stuff by you posting your favorite real analysis problems from college, internet, textbook, dream, imagination, etc. It would be so helpful to get some comments this time, and please don't post the solutions, I'm just looking for something to solve. Thanks.
 
Mathematics news on Phys.org
What do you mean by real analysis? Measures and integrals, or do you mean not complex?
 
martinbn said:
What do you mean by real analysis? Measures and integrals, or do you mean not complex?
not complex, though I suppose there's no reason to exclude complex.
 
I don't think that real analysis is an essential prerequisite for complex analysis other than what you would know from a good calculus class. Real analysis concentrates on measure theory and sets/functions with bizarre properties, whereas complex analysis concentrates on functions with amazingly smooth behavior (EDIT: except around essential singularities).

(EDIT: On the other hand, I think that Real Analysis, measure theory, and Lebesgue integration is essential for any mathematician.)
I have always been a fan of Schaum's Outlines. They have a lot of solved problems and exercises. For their Real Analysis, I can only find an online PDF that requires some sort of payment.
 
Last edited:
I think "real analysis", as a precursor to topology or complex analysis, means "single variable calculus, but done rigorously with proofs".
 
Reply
  • Like
Likes FactChecker and docnet

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I Optimization problem with multiple outputs: impossible?
Replies
6
Views
2K
Interested in Joining My Polymath Project on Real Analysis?
Replies
8
Views
2K
Video Lectures for Upper-Level Mathematics
2
Replies
90
Views
119K
Help Needed: Supplementing My Mathematical Analysis Course
Replies
7
Views
4K
I'm looking for someone to talk to about mathematical physics
Replies
1
Views
657
I New Video Course on General Topology on YouTube
Replies
2
Views
3K
Analysis Good supplementary real analysis book
Replies
10
Views
5K
Courses Should I retake Real Analysis I?
Replies
8
Views
3K
Studying Am I Challenging Myself Too Much in Math Learning?
Replies
14
Views
2K
I Advice toward Mastering Challenging Vector Calc Problems
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top