Questions about studying mathematics without formal instruction.

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7
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583 views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
7
votes
0answers
141 views

Am I reading Bott - Tu right?

Summary: I'm finding Bott - Tu to be too brief and terse. I constantly have to look elsewhere to fill in details. This is not time-efficient. Am I missing something? If not - what other books do ...
6
votes
9answers
533 views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
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6answers
1k views

What math is necessary to learn manifolds?

I want to learn about manifolds, but I'm only a senior in high school and obviously have a while to go. I'm in AP Calc BC. What should I study to eventually learn manifolds? Linear Algebra? What ...
6
votes
4answers
855 views

Expanding problem solving skill

I have a great passion for Math but my lack in problem solving skill always keeps me away from the "good stuff". I always wanted to be better at Math and one of the things I figured out was to keep ...
6
votes
3answers
485 views

The Importance Of Good Teachers and Guidance In the Academics

I'm a first year student for a math degree. I'm very curious on how good students overcome their bad teachers in the journey of learning and grasping the courses material fully, all in the pressure of ...
6
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3answers
641 views

Mastering Math - Grade school- to College-level?

I'm having difficulty with my math, fractions and up. I used to understand it all, but it's been so long since I've touched the book (I finished it a couple of months ago, picked it up to review ...
6
votes
5answers
1k views

Coxeter's “Geometry Revisited” vs. “Introduction to Geometry”

Which of these two books should I read first? Is one of them more advanced than the other? I'm planning to use them to self-study geometry. Thanks.
6
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3answers
260 views

Beginning with math

I am studying computer science since 3 years now. It is really math heavy and I like it. However the problem that I have is that I never really had math in school it was too basic and I lack some ...
6
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5answers
3k views

Steps to Re-Learn Mathematic the right way

I was always branded weak mathematics back at school though i loved it. The reason was that I was not having many basics in maths. Due to this problem I stopped learning Maths after my 10th grade. But ...
6
votes
2answers
2k views

Self-study on probability.

What book do you recommend for self-study of probability theory? I have a rather significant gap in that area (in lame terms sometimes I feel I don't get it) and need to try (strugle more likely) ...
6
votes
4answers
437 views

Can a function with just one point in its domain be continuous?

For example if my function is $f:\{1\}\longrightarrow \mathbb{R}$ such that $f(1)=1$. I have the next context: 1) According to the definition given in Spivak's book and also in wikipedia, since ...
6
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3answers
173 views

How can I find all the solutions of $\sin^5x+\cos^3x=1$

Find all the solutions of $$\sin^5x+\cos^3x=1$$ Trial:$x=0$ is a solution of this equation. How can I find other solutions (if any). Please help.
6
votes
4answers
273 views

Beyond the Exercises? [closed]

I've entertained and become bored with quite a few interests, though mathematics has more or less been my central passion throughout my high school/middle school life. I've only recently started into ...
6
votes
2answers
201 views

What can I do with measure theory that I can't with probability and statistics

I've studied mathematics and statistics at undergraduate level and am pretty happy with the main concepts. However, I've come across measure theory several times, and I know it is a basis for ...
6
votes
6answers
162 views

Any ideas how I can rewire my brain such that $\varphi \leq \psi$ “obviously” means that $\varphi$ implies $\psi$?

The Boolean domain $B=\{\mathrm{False},\mathrm{True}\},$ can be viewed as a partially ordered set in two different ways. In the best approach, $\mathrm{False}$ is the least element and $\mathrm{True}$ ...
6
votes
3answers
725 views

Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
6
votes
4answers
1k views

Two Different Approaches to Self-learn Calculus

Here's my situation: I'm a computer science student who has taken Calculus I twice. Not less than a week ago, I finished a second semester of the class and felt entirely defeated finishing the final. ...
6
votes
2answers
418 views

Self-Teaching: Is Geometry the Nexus of all Mathematics?

Necessary prologue: I'd really like to become more fluent in the language of mathematics. I don't have a schedule that permits me taking a class and any on-line tutors that I find seem relatively ...
6
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2answers
103 views

Independence of sigma-algebras

Good day to everyone. While solving some problem of studying character I obtained some statement to prove, which is like following (this is my internal interest to prove it rigorously). Assume that ...
6
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3answers
679 views

How to fill gaps in my math knowledge?

Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge. As I think many people who explore math ...
6
votes
2answers
773 views

Learning math-oriented French

I'd like to read several papers which I find interesting, but they are all in French. I have no problem with taking a traditional French class or learning it via some other method. However, I realize ...
6
votes
1answer
248 views

What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
6
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2answers
612 views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
6
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2answers
110 views

Missing and parasite roots in the trigonometric equation.

I have this equation: $$\boxed{\cos(2x) - \cos(8x) + \cos(6x) = 1}$$ RIGHT And its right solution from the textbook is: $$ \begin{align} \cos(2x)+\cos(6x)&=1+\cos(8x)\\\\ ...
6
votes
1answer
153 views

How much Differential Geometry is needed to appreciate Algebraic Geometry?

I want to start self-studying Algebraic Geometry at some point in the near future. There are plenty of posts discussing prerequisites, but one thing I couldn't find a discussion of: How much ...
6
votes
1answer
459 views

What's the best way to teach oneself both Category Theory & Model Theory?

I've done a bit of reading around both Category Theory & Model Theory (CT & MT) as a novice in each field. I'm interested in how they might combine, particularly when applied to Algebra. [So ...
6
votes
1answer
242 views

Basics of schemes and morphisms of schemes

I'm currently reading through Hartshorne, and have come across a few things that have left me wondering. (i) Somewhat pedantic, but also because I don't actually know the answer, (in Example 2.3.4) ...
6
votes
2answers
318 views

Filling the gap in knowledge of algebra

Recently, I realize that my inability to solve problems, sometimes, is because I have gaps in my knowldge of algebra. For example, I recently posted a question that asked why $\sqrt{(9x^2)}$ was not ...
6
votes
1answer
613 views

Importance of the Artin-Wedderburn theorem

I feel silly asking this, but what is the importance of the Artin-Wedderburn theorem in Algebra? In A First Course in Noncommutative Rings, T.Y. Lam calls it "the cornerstone of non-commutative ring ...
6
votes
1answer
200 views

Intuition behind proof and verification partially ordered sets

Hi everyone in the book that I read I have trouble to understand the argument of the proof at the below proposition. There is a lot of point which are left as exercises, which is great. One of these ...
6
votes
1answer
131 views

Soft Question: Suggestions on mathematics resources for problem solving.

I'm doing my final year of under graduation through distance education and would be appearing for entrance tests for various graduate schools in a few weeks. I am looking for a database of ...
6
votes
2answers
1k views

Prerequisite mathematics for studying data structures and algorithms

Forgive me if this seems trivial to you. But, I do need your advice. I am self-studying computer programming, now want to study Algorithms and Data Structures. All respected texts in A&DS talk in ...
6
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1answer
220 views

Capacity theory beginner resources

I'm currently studying a book on shape optimization: Variation et optimisation de formes: Une analyse géométrique By Antoine Henrot, Michel Pierre. The book introduces at some point capacity, and uses ...
6
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1answer
524 views

Supplementary exercises for Herstein's Noncommutative Rings

I've been studying from the book Noncommutative Rings by Herstein (not as a part of some official course), but unfortunately it doesn't contain any exercises apart from a few simple ones in the body. ...
6
votes
1answer
71 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
6
votes
1answer
1k views

What are the prerequisites for stochastic calculus?

I am not a math student, and only kind of picking up something whenever I need it. After emerged in the field of machine learning, probability, measure theory and functional analysis seem to be quite ...
6
votes
1answer
428 views

Philosophy of learning mathematics (combinatorics)

How does one learn mathematics in depth and well? I think I may be studying mathematics incorrectly, or I could be doing it a lot more efficiently/effectively. Sometimes I feel like I need every ...
6
votes
1answer
259 views

How to most efficiently remedy mathematical deficiencies

My spouse and I are currently both pursuing our undergraduate degrees. I'm double majoring in Computer Science & Mathematical Sciences and my spouse is double majoring in Economics & Finance. ...
6
votes
4answers
681 views

What are some good resources for brushing up on geometry and trigonometry?

I'm brushing up on my calculus, and geometry and trigonometry keep coming up. However, these are probably my weakest areas mathematically. Are there any good sites or free PDFs/ebooks that I can use ...
6
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0answers
87 views

Who wants to learn set theory? [closed]

So set theory is something I really want to learn. I found this document that I really like, except the fact that it doesn't prove all of it's theorems in with a lot of detail (a lot of times they say ...
6
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0answers
125 views

What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, ...
6
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0answers
138 views

Advice on learning mathematics

I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
5
votes
4answers
3k views

Multivariable Calculus books similar to “Advanced Calculus of Several Variables” by C.H. Edwards

I am currently trying to teach myself multivariable calculus using C.H. Edwards' "Advanced Calculus of Several Variables", but the text unfortunately doesn't have very many problems with solutions. ...
5
votes
4answers
2k views

Books, Video lectures, other resources to Teach Yourself Analysis

So my limited mathematics education has been especially ignorant of analysis. In this vein, I'd like to teach myself some of the introductory basics. I'm intrigued by sources that might contain ...
5
votes
4answers
106 views

Evaluate $\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$

I need to evaluate the integral: $$\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$$ for $0<p<1$. Unfortunately I do not know where to begin. I tried integration by parts but got nowhere ...
5
votes
3answers
578 views

Why are we interested in irreducible representation but not faithful representation?

I am reading some materials of representation theory (of a group). The motivation of representation theory is to represent (by a homomorphism $h: G \to GL(V)$, from the group $G$ to a vector space ...
5
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7answers
318 views

Good Number Theory books to start with?

I'm in Grade 11. I'm interested in elementary number theory and would like properly study it. I'm not intending to enter any competitions.
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3answers
497 views

Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.

I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one ...
5
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3answers
1k views

Help in self-studying mathematics.

Is this a reasonable list for who seek to learn mathematics by "self learning" program? and is it a well sorted list to follow? http://www.math.niu.edu/~rusin/known-math/index/index.html