Questions about studying mathematics without formal instruction.

learn more… | top users | synonyms (1)

7
votes
4answers
1k 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 ...
7
votes
2answers
652 views

Prerequisite reading for Weil's Basic Number Theory

I'm interested as to what would constitute prerequisite reading for André Weil's book Basic Number Theory. For simplicity (and generality), you can assume that the reader can read anything that ...
7
votes
4answers
6k views

Just how much proof knowledge is necessary to begin Spivak's Calculus?

I bought Spivak's classic Calculus a month or so ago, and after doing a few problems from the first chapter, it's become apparent that some type of foundational knowledge in formal maths and proofs ...
7
votes
3answers
90 views

How do I decide what problems and how many problems to do when I try to self study?

I am a math major at a relatively small college with barely any choice of classes to choose from so I have to supplement my studying with a lot of self studying. I usually have no problem getting ...
7
votes
2answers
93 views

How to show this inequality?

Show that $$-2 \le \cos \theta(\sin \theta+\sqrt{\sin^2 \theta +3})\le2$$ Trial: I know that $-\dfrac 1 2 \le \cos \theta\cdot\sin \theta \le \dfrac 1 2$ and $\sqrt 3\le\sqrt{\sin^2 \theta ...
7
votes
2answers
4k views

Rigorous Text in Multivariable Calculus and Linear Algebra

So I'm wanting a solid math book for Christmas. I have a solid background in Calculus and am currently working through baby Rudin. I really want a rigorous book dealing with multivariable calculus ...
7
votes
2answers
626 views

What is required to learn about algebraic geometry?

I want to learn about classical algebraic geometry. So what are subjects that are required to start learning about it? (Some preknowledge of algebra, commutative algebra?)
7
votes
3answers
686 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 ...
7
votes
2answers
2k views

Use of determinants

I have been teaching myself maths (primarily calculus) throughout this and last year, and was stumped with the use of determinants. In the math textbooks I have, they simply show how to compute a ...
7
votes
4answers
295 views

Advanced Mathematics

I am a high school student and would like to pursue a career in mathematics and I am hoping to find a serious explanatory book on math (geometry, algebra, calculus, functions and trigonometry) for ...
7
votes
5answers
2k views

Relearning Mathematics

First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these ...
7
votes
3answers
306 views

Is formal logic necessary for pure/“higher” mathematics?

I'm asking this as an autodidact who wants to learn math rigorously for its own sake. And I was just wondering if understanding proofs could be achieved without a formal grounding in symbolic logic. I ...
7
votes
2answers
619 views

How much rigour in proofs?

Just a quick pointer: you could probably get away with skipping to the last 2 paragraphs, as the rest covers my motivation for answering this question. Over this coming holidays I'm hoping to spend a ...
7
votes
1answer
382 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 ...
7
votes
1answer
107 views

Find $\sum_{k=1}^{\infty}\frac{1}{z_k^2}$

Let $z_1, z_2,\dots, z_k,\dots$ be all the roots of $e^z=z$. Let $C_N$ be the square in the plane centered at the origin with siden parallel to the axis and each of length $2\pi N$. Assume that ...
7
votes
5answers
588 views

Arithmetic mean is less than geometric mean (Spivak Calculus 3rd Chapter 2 Problem 22)

If $a_1, \ldots, a_n \ge 0$, the arithmetic mean $$A_n={a_1 + \cdots + a_n \over n}$$ and the geometric mean $$G_n = \sqrt[n]{a_1 \cdots a_n}$$ satisfy $G_n \le A_n$. As a first step to prove this ...
7
votes
3answers
127 views

Is there a better way to read proofs?

I'm finishing my undergraduate degree in 6 weeks and I'm pretty happy with how my education is coming along so far. I can write proofs, solve many different problems, and I even have some idea as to ...
7
votes
3answers
256 views

Self-study: what fractions of problems to solve?

I am self-studying measure-theoretic probability out of Billingsley's Probability and Measure. So far I have been trying to solve all the exercises. While the exercises are wonderful and I can ...
7
votes
1answer
450 views

Self Study of Fractals

I am looking for a book to self-study fractals with a certain criteria. I have checked out Getting Aquainted with Fractals. Note that Getting Aquainted with Fractals does not include ...
7
votes
1answer
506 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 ...
7
votes
3answers
175 views

Beginning of Romance

I am a 17-year old student in India, in the standard 12th grade. Recently, I found the fascination in mathematics, and I am eager to dig in further. Currently, the only textbooks I have are the ones ...
7
votes
3answers
1k views

Is there a correct order to learning maths properly?

I am a high school student but I would like to self-learn higher level maths so is there a correct order to do that? I have learnt pre-calculus, calculus, algebra, series and sequences, combinatorics, ...
7
votes
1answer
275 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) ...
7
votes
3answers
3k views

Functional analysis textbook (or course) with complete solutions to exercises

I am a Ph.D. student in economics and I plan to study functional analysis by myself either this winter or the next summer. I am currently looking for a textbook, and since I am studying it by myself, ...
7
votes
1answer
111 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 ...
7
votes
1answer
540 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 ...
7
votes
0answers
881 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
341 views

How much time is reasonable to complete baby Rudin? [closed]

I've been teaching myself math for more than a year. My current aim is towards algebraic topology and differential geometry. Apart from a messy (by which i mean some rigorous and some not) ...
6
votes
6answers
2k 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
5answers
4k 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. ...
6
votes
4answers
151 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 ...
6
votes
5answers
2k 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
votes
3answers
755 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 ...
6
votes
3answers
505 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
votes
3answers
700 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
6answers
4k 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
331 views

How can I pick up analysis quickly?

I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, ...
6
votes
3answers
281 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
votes
2answers
3k 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
719 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
votes
5answers
789 views

Materials for self-study (problems and answers)

I'm hoping to self-study Geometry, Algebra, Calculus, Vector Calculus, Linear Algebra, Probability and Statistics, and other intermediate maths. I've found the best way for me to learn is to work on ...
6
votes
3answers
184 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
1answer
151 views

Modeling Rain on a Windshield for various Speeds using Calculus

A question was recently posed to Click & Clack Talk Cars (http://www.greatfallstribune.com/story/life/2014/08/07/click-clack-rainy-day-raises-physics-question/13750681/). The topic is rain hitting ...
6
votes
2answers
528 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
180 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
1k 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
1answer
407 views

Learning Complex Geometry - Textbook Recommendation Request

I wish to learn Complex Geometry and am aware of the following books : Huybretchs, Voisin, Griffths-Harris, R O Wells, Demailly. But I am not sure which one or two to choose. I am interested in ...
6
votes
4answers
2k 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
3answers
845 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
459 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 ...