Questions about the process of learning mathematics, both inside and outside a formal environment, including learning strategies, recommendations for learning particular subjects, and studying habits.

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Getting Started in Bayesian Statistics [duplicate]

I want to start learning about Bayesian statistics. What resources would you recommend? If possible, I think for future readers it would be helpful if answers could be broken up into (1) overview ...
54
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6answers
3k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
2
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2answers
62 views

How to access the world's specialised knowledge? [closed]

This is a question that relates to almost all domains, I just happen to be passionate about maths. In my early teens, I used to believe that the path through all stages of standard education would ...
0
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0answers
22 views

Is there a broad map, guide or list of all or most of math's fields? [duplicate]

Has someone ever garthered all the different fields in maths (single variable function analisis, multivariable analisis, complex number analisis, number theory, graphs, succesions, etc) and made a ...
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8answers
7k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
7
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0answers
64 views

A List of Standard or “Cliche” Homeomorphisms [duplicate]

Learning topology has been hard. I just cannot see how some people can come up with complex functions that link one space to another, in a homeomorphic sense. The explanations are always "Well if you ...
3
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2answers
48 views

learning linear algebra [duplicate]

So I'm a college student that has taken 3 semesters of calc/diff eq/linear algebra and I think linear algebra has been by far my favorite course so far and I would love to know more in the subject, ...
2
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2answers
343 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
65
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8answers
13k views

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus ...
19
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6answers
7k views

Is memorization a good skill to learn or master mathematics?

I sometimes spend inordinate amounts of time memorizing math articles or theorems/proofs or formulas. My question is "am I wasting time?" and will 'active thinking' or 'working out problems' be faster ...
1
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3answers
4k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
1
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2answers
36 views

how to know when a particular proof is appropriate for the given problem?

The main trouble I am currently having in math is knowing when the use cases are appropriate in a proof. I see many videos where they seem to choose a strategy like proof by contrapositive or proof by ...
2
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1answer
101 views

Can we see natural deduction rules as functions or even as formal grammars?

Is there a way of seeing natural deduction rules as functions or even as formal grammars, maybe context-free grammars or Lambek grammars? It seems quite "easy" to see the rules as functions which take ...
15
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2answers
5k views

How to improve mathematics for Programming Contests?

You might close this question or downvote it, but I can't stop myself from asking the experts of mathematics who solve thousands of math problems. I'm a C++/C programmer who wants to improve his ...
0
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0answers
31 views

Coordinates of vector in new Basis

Find coordinates of vector $$\vec{u} $$in Basis $$ V={ (x−4y, x+y, 3x+y, x+y): x,y ∊ R} , \vec{u} =(−2, 6, 9, 2) $$ How can I do this? I found only examples for basis with explicit vectors.
25
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4answers
2k views

What are the dangers of visual exposition of mathematics?

I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition ...
5
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0answers
88 views

How can I learn Math intuitively? [closed]

I am currently a Junior in High School. I am in an Intermediate Algebra class, but my teacher does not always explain things in a way I can understand. I like to learn Math intuitively, but my teacher ...
4
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1answer
1k views

Vector spaces - Multiplying by zero scalar yields zero vector

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space related axioms. ...
1
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1answer
42 views

where to find good examples of combinatorics (online resources only please)?

one of the most beautiful/hard things in the study of combinatorics is the fact that is not just about memorizing 4 or 5 formulae but developing a whole reasoning ability. Such thing can only be ...
2
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2answers
78 views

How should I start solving a calculus problem? [closed]

There are so many books teaching how to take derivative and integration of a function. I think I'm good enough (enough for me lol) in those parts, my problem is that I can't start solving a question ...
12
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5answers
6k views

Why is it that when proving trig identities, one must work both sides independently?

Suppose that you have to prove the trig identity: $$\frac{\sin\theta - \sin^3\theta}{\cos^2\theta}=\sin\theta$$ I have always been told that I should manipulate the left and right sides of the ...
63
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20answers
48k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
0
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1answer
16 views

Use of the Bezout Theorem in the Proof of Field Extension

Let $p$ be a prime number. Let $F$={0,1,...,p-1}. += addition mod p .= multiplication mod p The only nontrivial thing to check is the existence ...
0
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1answer
64 views

Understanding Proof that $\mathbb{Q} \left( \sqrt {2}\right)$ is a field. [duplicate]

Prop. $\mathbb{Q} \left( \sqrt {2}\right)$ under usual properties, i.e., $\mathbb{Q} \left( \sqrt {2}\right)$ is a field. Proof. (Step of multiplicative inverse of $\mathbb{Q} \left( \sqrt ...
0
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1answer
21 views

Understanding of example of subspacee

Let F be a field. Then, { (a,b) $\in$ F: $\alpha$a+$\beta$b=0} is a subspace of FxF for any $\alpha$, $\beta$ $\in$ F. My question is that can be FxF is a subspace of f? If not, why?
71
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3answers
3k views

Is there a definitive guide to speaking mathematics?

Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres ...
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3answers
41 views

Understanding Defiinition of Vector Space

Let $F$ be a field. A vector space over $F$ is a set $V$ together with $+$,$\cdot$ satisfiyng: $$+: V \times V \rightarrow V$$ $$\cdot: F \times V \rightarrow V$$ with usual properties. My ...
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0answers
47 views

How do I memorize mathematical proofs?

I first started wanting to know about the derivation of theorems because certain ones help you memorize the theorems better. But as I take harder math classes, it turns out better for me to use ...
1
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2answers
83 views

Should non mathematicians learn mathematics “just in time” or ahead of time? [closed]

I am wondering how someone that is not exclusively interested in mathematics (but nevertheless aims to become a decent applied mathematician), but for example, a theoretical computer scientist, should ...
0
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2answers
42 views

Understanding a problem

Note that these from linear algebra notes. İt was defined fields, showed $\mathbb{Q}$ is a field. Then, below-mentioned qustion was proved. Yet, I didn't ask what happened. Can you explain? What ...
16
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1answer
243 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
2
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2answers
114 views

Diagnosing essential Classical Mathematical Analysis I knowledge needed for II

I need to take Classical Mathematical Analysis II (Chapters 7-10: Sequences & Series of Functions, Special Functions (Exp/Log/Fourier/Gamma), Functions of Several Variables, Integration of ...
66
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11answers
8k views

How do people who study intensely abstract mathematics “imagine” or understand the concepts they are studying or being taught? [closed]

This question is probably to the actual people who study such mathematics, rather than any "third-party". I haven't studied any such mathematics, but I can imagine that some (probably most of it) of ...
11
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4answers
684 views

How can I explain topology to my grandmother?

I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" ...
9
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6answers
11k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
13
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2answers
20k views

Tips for an adult to learn math — from the beginning. [closed]

First let me start with I am an adult and I can't do simple maths. I some how got through all of my math courses in University (after several attempts) but I honestly couldn't tell you how... I ...
4
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1answer
72 views

What is the significance of “Homomorphism”?

Certainly Homomorphism is a prerequisite to establish an “Isomorphism”(Bijection), but what does a Homomorphism tell independently when it is established between two sets? Homomorphism relates ...
1
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2answers
130 views

Should I continue trying to solve Spivak or pick up a lighter book?

Some background: I have no mathematical maturity. Last year I completed my schooling and the only time I picked up a math/science book was when exams were due, needless to say I haven't actually given ...
1
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1answer
91 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
56
votes
4answers
7k views

Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
1
vote
2answers
142 views

How much group theory is required before undertaking an introductory course on Galois Theory?

How much knowledge of group theory is needed in order to begin Galois Theory? Which topics are most relevant?
19
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3answers
1k views

Working habits in mathematics [closed]

Short version of my question: What are good and motivating working habits for a mathematician? N.B. There are similar questions to mine: see this (how to read maths) or this (efficient study) or this ...
5
votes
3answers
423 views

How to determine if I'm talented enough to study math? [closed]

After getting Bachelor's degree from Computer Science I changed my field to Applied Mathematics. The previous degree was mostly programming-oriented, so I know quite a lot about software engineering, ...
5
votes
2answers
401 views

Numerical analysis, differential equations, complex analysis for statistics

I am a student of the Statistics Department. And now I can choose a subject from such list: numerical mathematics (analysis), differential equations, complex analysis, real analysis. Can you please ...
3
votes
1answer
1k views

Best way to learn from textbooks that have the Theorem-Proof format?

I've always loved the theorem-proof format in textbooks, e.g. Hardy and Wright's Introduction to the theory of numbers. However, the problem is that I can't remember anything I read in this format ...
8
votes
2answers
556 views

I like math, but can't keep up with the pace. [closed]

I'm a math major. I like math. I'm comfortable with it. I'm considering to do a PhD. The thing is I always fall behind. I can't keep up with the professor, can't turn in satisfactory homework in ...
5
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3answers
483 views

Map of Mathematical Logic [closed]

My undergraduate University does not offer advanced courses on logic, I know truth tables, Boolean algebra, propositional calculus. However I want to pursue Mathematical Logic on the long term as a ...
3
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3answers
137 views

Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
1
vote
2answers
126 views

How do mathematicians come up with beautiful equations [closed]

In Linear regression for example, we can find weights as following: $\hat{\beta}=(X^{T}X)^{-1}X^{T}y$ how someone invented this? I mean how do they transform a problem to such an equation. And ...
4
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4answers
758 views

Write on my own my first mathematical induction proof

I am trying to understand how to write mathematical induction proofs. This is my first attempt. Prove that the sum of cubic positive integers is equal to the formula $$\frac{n^2 (n+1)^2}{4}.$$ I ...