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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3answers
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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
37 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
69 views

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

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
37 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 ...
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0answers
63 views

Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read? [closed]

I've noticed that many books that are difficult to read are considered some of the best. Why does hard to read indicate that it is rigorous? For example: Rudin, Apostol, Lang, Hungerford, Ahlfors, ...
2
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2answers
110 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 ...
3
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1answer
57 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
96 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
58 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 ...
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2answers
136 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?
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3answers
216 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
319 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 ...
8
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2answers
506 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 ...
1
vote
2answers
114 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 ...
3
votes
3answers
107 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
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0answers
55 views

Is propositional logic enough to study real analysis?

Is it necessary to study relational logic before starting real anylisis(from Bartle and Scherbert) or propositional logic enough? Also for topics like topology and differential geometry is ...
2
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2answers
179 views

Theoretical and applied math help - what and why? [closed]

(Edit: If you wish to skip the prologue, you may go straight to the questions in the last few paragraphs.) I'm not very far ahead at the moment (going to begin my undergraduate years after next ...
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1answer
36 views

What can I do after calculus I besides calculus II? [closed]

I'm a high school senior that's just about finished studying calculus I. I probably can't take AP calculus BC, and I don't want to learn calculus II over the summer or during my spare time. I would ...
1
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2answers
47 views

Interpretation of a statement that I think I can prove by mathematical induction

I want to prove by mathematical induction the following statement: for any sequence (a_k) of non negative real numbers holds that: $$(1+a1)(1+a2)...(1+a_n) >= 1 + a_1 + a_2 + ... a_n$$ I think ...
4
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4answers
751 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 ...
2
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1answer
104 views

Learning how to prove by mathematical induction for the first time [duplicate]

So, I have to prove this by mathematical induction and I have never done it! $$\sum_{i=1}^n i^2 = n(n+1)(2n+1)/6$$ However, I have learnt better the theory behind this way to prove statements and ...
3
votes
2answers
82 views

Natural proofs of theorems or exercises [closed]

Some mathematicians wants to hide their reasoning and proof process so that they appear smart. As most of the mathematics lovers I am not a genius and this is why I hate the magical proofs because ...
1
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0answers
45 views

Undergrad looking for study material/advice for applied mathematics.

I am an undergraduate math student (junior) who is looking to get a masters degree in Applied Math. I like pure math, but I want to use my education to get a great-paying job. Here are a few questions ...
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4answers
1k views

How do you resist thinking about you may not be able to go further in mathematics? [closed]

I believe that every mathematical "apprentice" more or less once found that some stuff that had been unclear somehow became clear; for example, some books might be unaccessible to you two years ago ...
1
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1answer
71 views

New to Abstract Algebra, need guidance [closed]

I am new to Abstract Algebra. How should I begin learning it. On the face if it, it doesn't look easy to me.I have bought the book by Prof. Gallian. Is there any other book or any videos which I can ...
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0answers
106 views

Solutions for “What is Mathematics?” by Richard Courant

I am currently reading through Courant's "What is Mathematics?" Most of the time I am not taking the exercises too seriously, given that I am reading this for pleasure, and that often my solutions are ...
0
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4answers
106 views

How to study Linear Algebra when lecturer moves too fast [closed]

Our Algebra and geometry class is moving so fast the lecturer does not have enough time to cover all material in class, and he is not very pedagogical at that. Trying to fill in gaps through reading ...
4
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3answers
86 views

What is the equivalent of musical ear training with regards to studying mathematics

When one aspires to be a professional musician, it is made clear that ear training is a very valuable skill that must be cultivated on a daily basis. The student is advised to put in the time and ...
1
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1answer
108 views

Is the i-e principle for symmetric difference useful?

Let $E$ be a set and $A$ and $B$ two subsets. We may define the symmetric difference of $A$ and $B$ by setting : $$A\Delta B:=(A\cup B)\cap (A\cap B)^c $$ There are many interesting things about ...
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7answers
1k views

Strategy for reading math books, is it better to prove the theorems yourself or just read them?

Context: I'm self-studying some mid to upper level undergraduate math subjects. For example, right now I'm reading Munkres' Topology book. Usually, the approach I use is to go through the book in ...
-5
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1answer
117 views

If you don't read A to Z, then how can you discover the idea? [closed]

[Source:] Rutgers University Professor [Henryk] Iwaniec and his friend, John Friedlander, a professor at the University of Toronto, read with increasing attention. “In these cases, you don’t read A ...
2
votes
1answer
102 views

Difficult to read about different subjects simultaneously, should I leave one for now? [closed]

I learn math by reading books. Usually I read 3 books (about 3 different subjects) simultaneously and switch focus every couple of days. The books i'm studying right now are Rudin's functional ...
2
votes
1answer
91 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 ...
2
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2answers
51 views

How to retrieve the expression of $a^3+b^3+c^3$ in terms of symmetric polynomials?

I recently had to find without any resources the expression of $a^3+b^3+c^3$ in terms of $a+b+c$, $ab+ac+bc$ and $abc$. Although it's easy to see that $a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)$, I couldn't ...
2
votes
2answers
306 views

Why is math so difficult for me? [closed]

I'm an aspiring software engineer and currenly in college for computer science. For some reason, no matter what I try, math is so unbearably difficult and indecipherable until I design a program for ...
2
votes
3answers
137 views

How do I figure out my math aspirations? [closed]

I am really confused. Here's my present situation: I'm 18. I am about to start a computer science degree this August--going there only coz my parents want me to. I know most teachers for undergrads ...
0
votes
1answer
97 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
3
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2answers
82 views

The Monty Hall problem - convincing a skeptic

I have lost count of the number of times that I have been debating the solution of the Monty Hall problem with someone. Recently I had a long conversation with a colleague, who didn't seem to buy ...
2
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1answer
70 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
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0answers
34 views

Sample complexity of coin bias problem

I am reading a paper involving learning in Multi-armed bandit case (its okay if you don't know what that is. Just trying to give context here.) To give sample complexity lower bound, they reduce their ...
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1answer
98 views

Math without notation [on hold]

Are there any researchers that try to develop learning materials to teach the core mathematics knowledge without using notation (and instead just plain English -- preferably without images)?
13
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1answer
221 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
votes
0answers
134 views

How to learn problem solving strategy for Measure Theory?

I have taken both graduate level Algebra and Measure theory courses but found the latter much more difficult for me. I have put a lot effort on learning it by reading a few reference books and ...
2
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1answer
54 views

Matrix multiplication memorisation

So I'm writing an exam about matrices in a few weeks time, and I'd like to know if anybody has any tips about multiplying matrices.
0
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1answer
330 views

Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
1
vote
2answers
60 views

Representative Pedagogical Examples of Groups, Real Functions, Modules, etc.

In the preface of Munkres's Topology, he writes, Fortunately, one does not need too many counterexamples for a first course; there is a fairly short list that will suffice for most purposes. Let ...
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2answers
272 views

Learning modern differential geometry before curves and surfaces

What might one miss by learning modern differential geometry without first learning about curves and surfaces? I'm currently reading this book on differential geometry which starts with manifolds and ...
14
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2answers
670 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
15
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4answers
2k views

Is it necessary for one to understand analysis?

Is it necessary for one to understand analysis in order to pursue a career in mathematics? Basically, I am very weak at analysis. But the problem is that most of the topics listed in the syllabus ...
13
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1answer
189 views

How to stay productive while you are studying math? [closed]

Not sure that this question is a good fit for this site, but I will try. When I am working through a chapter of a mathematical book first two hours are normally very productive (easily remember ...