Intereting Posts

Integer solutions of $xy+9(x+y)=2006$
which of the following metric spaces are complete?
How many fours are needed to represent numbers up to $N$?
Separated schemes and unicity of extension
Rank of a $n! \times n$ matrix
Why are box topology and product topology different on infinite products of topological spaces?
How can I show that $\left|\sum_{n=1}^\infty\frac{x}{n^2+x^2}\right|\leq\frac{\pi}{2}$ for any $x\in{\bf R}$?
Different way solving limit $\lim \limits_{ x\rightarrow 0 }{ { x }^{ x } } $
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of proper subspaces of $V$
Ring germs of $C^{\infty}$ functions on the real line
find all self-complementary graphs on five vertices
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
nilpotent elements of $M_2(\mathbb{R})$, $M_2(\mathbb{Z}/4\mathbb{Z})$
Integration using residues
Notation and hierarchy of cartesian spaces, euclidean spaces, riemannian spaces and manifolds

Since math students will be stuck on some math at some point, what strategies or tips can help

(to assuage this recurrent reality of maths)?

Certainly, this wonderful website helps; here: one can ask questions, interact with different people, be referred to other information. Still, to what else can be one resort?

I thought to start with some quotes from the following two articles:

- In what order should the following areas of mathematics be learned?
- Perspectives on Riemann Surfaces
- Math Textbooks for High School
- Rudin against Pugh for Textbook for First Course in Real Analysis
- How to study math to really understand it and have a healthy lifestyle with free time?
- “Advice to young mathematicians”

[Source:] As research mathematicians, Littlewood and Poincaré knew the value of letting a problem go. They both structured into their lives time for allowing the attention to disengage from the level of actively thinking about a problem. Littlewood went for walks in the country. Poincaré went on a geology excursion. And occasionally, with good luck, the sudden flash of deep inspiration occurred.

[Source:] ■ The first theme has to do with sleep and the role it plays in doing mathematics and AHA! experiences. Many of the participants commented at one time or another about the phenomenon of waking up to a solution, either in part or even fully formed.

■…he discusses how “a bridge gets built between two apparently unrelated fields”.

■ Certain gaps in knowledge needed to be filled and my main role was to feel that these gaps could be filled. – Dick Askey

- Is linear algebra laying the foundation for something important?
- Rudin: Problem Chp3.11 and need advice.
- If there are obvious things, why should we prove them?
- Is the exclusion of uncountable additivity a drawback of Lebesgue measure?
- Is it morally right and pedagogically right to google answers to homework?
- Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?
- Why there is no sign of logic symbols in mathematical texts?
- How to define the operation of division apart from the inverse of multiplication?
- A continued fraction for $\sqrt{2}\Bigg({e^\sqrt{2}-1 \above 1.5pt e^\sqrt{2}+1 }\Bigg)$
- What's your favorite proof accessible to a general audience?

This, probably, is a more appropriate answer to: “Strategies – What to do when stuck on some math *problem*“, but I thought it was still worth mentioning.

I’ve always thought that section 2.1 of this book is a rather nice and concise list of concrete advice regarding how to solve problems in analysis, particularly useful–I think– for students who might not have a large experience in tackling proofs. If I’m stuck on a problem, having a read through it, sometimes, gives me an idea of what else I can try.

I know this is an old post, but stuck at math, or stuck on a problem, this is a timeless issue. I’m trying to personally close the gaps that keep me from getting better marks and I think that while Polya, mentioned above, is a great book, and a wonderful resource, it was written first in 1945 and then a second edition was published in 1957. And while the techniques used for old problems is almost canonical (geometry = Euclid), the way we speak in about math has changed. So we need a younger, more contemporary voice. I started with Polya. But it is hard for me to relate to. There had to be another resource.

So, instead, I can recommend to anyone reading this and looking for help on this topic, take a look at Terrence Tao’s book “Solving Mathematical Problems” and work through the problems. And really try to absorb the process as you do it. I use spaced repetition to remember definitions and theorems, and an index card with a succinct list of steps (there are 8 or 10, if I recall) one can commit to memory to prompt oneself when struggling on a proof or exam question. Each of the worked examples considers the value of all the data you’ve collected on the issue, trying to get the reader to internalize the questions to ask at each step.

I hope this helps any new viewer of this thread.

- About the identity $\sum\limits_{i=0}^{\infty}\binom{2i+j}{i}z^i=\frac{B_2(z)^j}{\sqrt{1-4z}}$
- Examples about that $\exp(X+Y)=\exp(X) \exp(Y)$ does not imply $=0$ where $X,Y$ are $n \times n $ matrix
- Does one of $L^\infty$ and $L^p, p \in (0, \infty)$ contain the other?
- How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
- How can Zeno's dichotomy paradox be disproved using mathematics?
- Cauchy Sequence that Does Not Converge
- How prove this $I=\int_{0}^{\infty}\frac{1}{x}\ln{\left(\frac{1+x}{1-x}\right)^2}dx=\pi^2$
- What's an example of a vector space that doesn't have a basis if we don't accept Choice?
- How is this possible to convert a long string to a number with less characters?
- Finding $\lim_{n \to \infty} \frac{\sqrt{n!}}{2^n}$
- How to prove or disprove statements about sets
- Characteristic time?
- how to prove this extended prime number theorem?
- Correlation in Bernoulli trial
- Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$