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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17 views

Looking for Comprehensive Integration Techniques Tutorial

I am trying to improve my skills and I usually learn best by attempting problems just barely above my skill level then reading the solution. Does anyone know where I can find structured integration ...
4
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1answer
192 views

Is this study plan sufficiently general, or overly specialized? [closed]

My current study plan is in order below. I will be completing these textbooks in this order one at a time. I have been told that I don't have textbooks in my plan that approach topology in a general ...
10
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0answers
135 views

How beginner researcher or ph. d student should learn new concepts?

I hope this question is o.k for S.E. M. When some one is reading book(monograph); possibly helpful in his/her research, and content is large enough; At the first glance it seems very frustrating and ...
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1answer
27 views

How can i learn when to use which multiplication rule: Probability

Hey guys im studying for a math exam and was wondering if anyone has some easy techniques to remember in what kind of scenario to use these equations. These are I believe called multiplication rules. ...
3
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1answer
51 views

Is probability theory useful in electrical engineering

I have a two week holiday after finishing this semester and I was hoping to study something. Ideally, I would like to study something that I can benefit from in any upcoming courses I take. I'm ...
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0answers
45 views

Can any one recommend a way to “quickly” learn a subject?

I would love to read a well written book on a subject - provided that I have the time. But sometimes we do not need to become experts on a particular field but still need the basics. For example, a ...
2
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1answer
71 views

How can I learn to recognize the obvious questions?

I have heard and seen several references to "obvious questions", "obvious axioms" and other "obvious" things (I am not referring to obvious results!). Now, in a seminar I am taking, at the end of each ...
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1answer
60 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 ...
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0answers
77 views

How to deal with a lack of ability to apply ideas in math?

I am currently studying Theoretical Computer Science, but as a Computer Science student who does not have a formal background in mathematics, past A Level (High School), I find that the ideas I learn ...
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2answers
48 views

Optimizing a box

I'm learning the use of derivatives and I have found a problem: Supposing we want to build a box of $4000\, \textrm{cm}^3$ of volume without top and a square base. Which are the measures so we ...
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2answers
46 views

Is it possible to gain intuition into these trig compound angle formulas - and in general, final year high school math?

Does anyone have any insight into the trig sum and difference formulas? The formulas in themselves are very elegant, but I don't really like the proofs that have been given, even the geometric proofs. ...
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0answers
256 views

IMO programs of different nations?

We have a good team in the IMO, and this year I can, and probably will, be part of it. Since we as a country do not have a public training programme, I have to consult the training programms of ...
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2answers
41 views

Find the equation of the parabola given the tangent to a point and another point.

I have a problem with derivatives, I've been trying to solve but I was not able to do it. A parabola is tangent to the line $3x-y+6 = 0$ in the point $(0,6)$ and goes through the point $(1,0)$. ...
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3answers
85 views

I want to study higher mathematics. Where do I start?

Since last year, I've been interested in higher mathematics and don't really know where to start and don't know what knowledge I still need to obtain, before being able to understand the concepts. ...
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2answers
87 views

Logical order to understand math? [closed]

Imagine a 30 year old human coming from the wild, never visit a school and nether came in touch with math what so ever. And now imagine this person wants to learn math on an academic level. But where ...
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0answers
23 views

Books or notes focusing more on the intersection between manifolds and topology?

I try to prepare for the qualify exams, and find that the problems of geometry part are quite interesting. In the past, I just learned some elementary things on manifolds and algebraic topology ...
4
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0answers
53 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
4
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0answers
66 views

How to select good exercises?

I'm studying on Rudin "Principles of of Mathematical Analysis" which I begin to find as a good and complete reference. I wonder how many exercises shall I do at the end of each chapter ? In case of ...
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3answers
33 views

Is this derivative correct?

I'm newbie at Calculus, so I'm doing some exercises of derivates, I know by the formula: $f(x) = \sqrt u$ $\frac {df(x)}{dx} = \frac{u'}{2 \sqrt u}$ that the derivate of the next function is: ...
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2answers
67 views

Path to 3d Mathematics programming, where to start?

This might read like duplicate of this question https://math.stackexchange.com/search?q=where+to+start However since that one wasn't answered, and I have a more specific problem in regards to ...
4
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1answer
103 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and ...
2
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1answer
31 views

Website for Practice?

I'm a high school student eager to practice difficult questions of various topics in preparation for an exam at the end of the year. Does anyone know a website which has challenging problems which ...
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1answer
33 views

How to expand this polynomial division?

My Physics teacher gave me a problem and its solution, what I have todo is to expand the solution, but when I do it I do not get to the same solution he says is the right one, here is the problem: ...
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2answers
91 views

Books/subjects for proof practice

So I want to practice writing proofs. I've studied general proof-writing but now I want to learn how to apply that to mathematics. From what I understand, the best and most accessible subjects for ...
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0answers
48 views

Working on strengths vs. weaknesses as an undergraduate student

I realize there's a lot of general advice on this site and elsewhere about studying mathematics, but I couldn't find anything about this, so I've decided to ask: as an undergraduate student, I'm ...
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5answers
1k views

Self-learning mathematics - help needed!

First, I apologise for the nebulous nature of my title but I can't adequately explain myself concisely. I am about to start an MSc in pure maths after a fairly shaky undergraduate degree. I am very ...
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0answers
58 views

How to approach real analaysis

I'm just starting first year in university in Europe and here there there is no Calculus, instead you jump right into Analysis. The trouble is, for some time I self-studied through US style books and ...
2
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1answer
101 views

Vector spaces - Multiplying by zero vector 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 axioms. Axiom ...
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0answers
44 views

Vector spaces - Multiplying by $-1$ yields inverse element of vector addition.

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

Bridging the Gap Between Implicit Understanding and Formal Math

I use set theory on an implicit basis as a programmer; however, it's recently become necessary for me to expand into the formal world to explain my intent to decision makers that don't operate at a ...
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0answers
39 views

How do you look for classic/normative/standard books about an established branch of mathematics?

If you want to immerse yourself in a branch of mathematics (e.g. linear algebra and linear optimisation) which is new to you, then you often look for standard books which you can rely on. You could ...
2
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0answers
54 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
3
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0answers
161 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. ...
4
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1answer
55 views

Vector spaces - If an addend adds nothing, then the addend is the zero vector.

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. With one exception, the following proof is solely based on vector ...
1
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0answers
57 views

Another proof of uniqueness of identity element of addition of vector space

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 axioms. Axiom ...
3
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5answers
493 views

Proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. Proof of uniqueness of identity element of addition of vector space ...
3
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0answers
83 views

Attemping Qualifying Exam Problems — and failing

My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education ...
3
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3answers
72 views

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$?

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$? I am learning trigonometric identities one identity I have to proof is the next: $ (1- \sin \alpha + \cos \alpha)^2 = ...
6
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2answers
234 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
2
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2answers
68 views

Motivational example for complex numbers

Years ago I was introduced to complex numbers. In class we had been talking about the cubic polynomial and its solutions. At one point we saw an example where, when using the formula, one had to stop ...
14
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5answers
727 views

Understanding mathematical texts

Please could you comment on following: I always wanted to know what mathematicians mean by "understanding a piece of mathematics". For example, I have just finished the second chapter from Rudin's ...
2
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0answers
94 views

Most Suitable Book after Kline's Calculus?

I've been working through Morris Kline's Calculus: An Intuitive and Physical Approach and it's an absolutely excellent book for self-studying applied single-variable (and some multi-variable) calculus ...
4
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0answers
88 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?
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1answer
85 views

Book recommendations for someone interested in higher mathematics?

Background: I am currently studying physics and except for high school mathematics I have experience with linear algebra, single- and multivariable calculus, differential equations (mostly ODE's, but ...
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0answers
27 views

Are there online-platforms where to find people for joint learning and discussions?

After quite some time in academia I ended up in a nice company but the math to use is not really demanding. Hence I am still reading and working a bit on some university level math. It's roughly at a ...
2
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1answer
100 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering ...
3
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1answer
427 views

Do only certain people exceed at math well? [closed]

It's obvious if you look around that math has always been one of the toughest subjects in all areas, from federal-traditional public schools to simply people learning it as an autodidact, hobby, or as ...
0
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1answer
41 views

The value of to fill the gap in the proof

I have studied a paper "On Finite Groups with Given Conjugate Types I" recently. The author use many words like "obviously", "clearly", "trivial", etc. in his proof. But these "obviously" implication ...
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1answer
44 views

Intuition or wisdom for stability and instability properties of locally linear system. Boyce, p513, Table 9.3.1

Our instructor requires us to memorize this table for our differential equations exam. So I wonder if anyone has some deeper intuition or observation to help with this? For example, I noticed ...
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2answers
67 views

I still forget concepts even after answering numerous math problems

Note: this is particularly aimed at high-school/entry level college problems When I'm learning a new topic: 1) I read the theory given in the textbook at the start of each topic 2) proceed to read ...