Questions about studying mathematics without formal instruction.

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1answer
205 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
135 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 ...
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2answers
2k 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
234 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
539 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
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1answer
474 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
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1answer
276 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
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4answers
720 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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2answers
177 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 ...
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0answers
94 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
139 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
148 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
3answers
632 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 ...
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7answers
377 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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4answers
201 views

Studying mathematics: Is proving things yourself worth the time?

When studying mathematics, is proving things yourself (before reading the proof given in the text) worth the time? This approach takes significantly longer than simply trying to follow along, but you ...
5
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 ...
5
votes
4answers
212 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
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
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4answers
281 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 ...
5
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3answers
242 views

Laplace transforms: Convolution

Find $$1*1*1*\cdots*1\quad n\,\,\text{ factors}$$ that is, a function $f(t)=1$ convolution with itself for a total of $n$ factors. Would anyone mind helping me? I have no idea what I should do. ...
5
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2answers
184 views

What all maths do I need to know to become good at machine learning.

I am a computer science engineer and I took a couple of maths classes in my first year they were on Fourier series(not transform) partial differential equations, vector calculus, infinite series ...
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5answers
261 views

Leisure reading for an undergraduate student

I am a freshman at a local university. I never really had much passion for math, but I always did well in math exams . I attribute this lack of passion to rote learning/emphasis on methods/formulas ...
5
votes
1answer
146 views

where to start reading theory of logics?

I am a student who is working Lie Theory. I want to start read theory of logics. I just need some reference and I have few questions regarding this, i) will studying theory of logics will improve my ...
5
votes
4answers
615 views

Self-learning Mathematics

My question is very elementary, but I hope that you will endure it. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ...
5
votes
1answer
196 views

Fundamental theorem Galois Theory

From time to time, I try to give my non-mathematician scientist friends descriptions of important theorems that I come across. One friend, watched a video on Galois and now I'm at a loss on how to ...
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6answers
167 views

When learning maths, should I review past topics?

So I've been learning maths from online video lectures and books for some time now and, as is probably quite natural, I have forgotten some of the stuff I've already read through. That'd be mostly ...
5
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1answer
307 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 ...
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2answers
210 views

Books on the history of foundations of mathematics?

Can you point me to some books on the history of the foundations of mathematics? At the moment I'm searching for something light because of my lack of mathematical maturity and also the fact that I'm ...
5
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2answers
172 views

How effective is Wikipedia for first line of attack?

I am learning some pretty disconnected concepts of mathematics for a project I am working on. I was reading about matrices and suddenly had to know about Markov Chains and that lead me to read about ...
5
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3answers
6k 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 ...
5
votes
2answers
348 views

In what order should mathematical fields be learned? [closed]

This could be considered a broader version of this question, with all fields. I know that when high-level maths are reached, the fields being to split quickly (i.e. specializing in this type of ...
5
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5answers
923 views

How might I refresh high school level mathematics and extend upon it much further?

I did well at Mathematics at school (top 0.1% in the country, approximately), however I stopped studying it when I was 16. Since then I've studied a couple of highly specific mathematics modules in ...
5
votes
2answers
137 views

Easy exercise (hint) Real Analysis

I've been stuck for a while with this problem. I suppose is something very easy, but I cannot figure out yet the correct approach. I'd really appreciated not a complete solution just some hints ...
5
votes
2answers
126 views

Looking for explanation of bound on Dirichlet's L-Function

I am reading Stein and Shakarchi's Fourier Analysis text and the proof Dirichlet's theorem and I am looking for clarification on how he derives the following for large $s$, $\lim_{s\to\infty}$ and ...
5
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7answers
916 views

What should I learn next for pure math?

I can do basic single variable calculus which is essentially all you do at A Level in the UK. I also just read "What is mathematics?" by Richard Courant which I found very good. I would like to know ...
5
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2answers
297 views

Going back to the basics? [closed]

I'm currently in my second year of college majoring in comp sci and I haven't really taken any math courses yet except pre-calc. In high school, I thought of myself as a pretty good math student and ...
5
votes
1answer
404 views

Want to learn differential geometry and Riemannian geometry by myself

I want to follow a Ph.D. programme on geometric analysis. The main focus are Monge-Ampere equations and convex level set of $p$-harmonic equations. The theory of PDEs is very familar to me. However, I ...
5
votes
2answers
542 views

Math for a high school junior?

I don't find the math taught at my school too challenging so out of personal interest I teach myself other fields of math. I was wondering if you could recommend some areas with a bit more complexity? ...
5
votes
2answers
196 views

The area problem!

We have to find area of the quadrilateral formed by joining the point of intersection of the four quarter circles that are drawn from each vertex in a unit square. $\hspace{4cm}$ The challenge is ...
5
votes
4answers
3k views

Where can I download Discrete Mathematics lecture videos?

Good morning, I'm doing a course in Discrete Mathematics (so far: Four Colour Theorem, Intro Graph Theory, Intro Logic Theory, Intro Set Theory and Intro Proofs) at University, but unfortunately they ...
5
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1answer
72 views

The Use of Sound in Mathematics. [on hold]

I'm not sure that this question is appropriate here. There's a good chance it's too opinion-based. If that's the case, I'm sorry. I was sat in a research seminar recently and wondered whether it'd be ...
5
votes
1answer
85 views

What math have I missed as an Engineeering graduate? [closed]

To explain, I have a Master's in Engineering from a well known university. We did a wide variety of mathematical topics, vector calc, perturbation methods, numerical methods, linear algebra, discrete ...
5
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3answers
55 views

Area preserving transformation in a higher dimensional space is unitary.

In $\mathbb{R}^3$, a linear operator $Q:\mathbb{R}^3 \to \mathbb{R}^3$ preserves the area of parallelograms: that is, given $x,y\in \mathbb{R}^3$, the area of a parallelogram formed by $x$ and $y$ is ...
5
votes
1answer
75 views

$F,G \in \text{End} (V)$ share the same eigenvalues for $F \circ G$ and $G \circ F$

Problem: Let $V$ be a finite dimensional Vector Space over a field $\mathbb{F}$ and $F,G \in \text{End}(V) $ Show that $F \circ G$ and $G \circ F$ have the same Eigenvalues $\lambda$ My ...
5
votes
1answer
184 views

When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
5
votes
1answer
178 views

Calculation of sum by using residue theory

I am studying an example about the calculation of a summation by using residue theory. I understand how to calculate the sum in general -the frame of the solution way-, but I dont know how some parts ...
5
votes
2answers
688 views

Strategy to improve own knowledge in certain topics?

My background is physicist/engineer, and at university we studied only particular topics in mathematics. Some of the courses were never used and faded away with time, and I need to refresh the ...
5
votes
2answers
442 views

How can I find videos of mathematics at graduate level, especially on linear algebraic groups

I am studying mathematics by myself, and I find it very helpful to watch online course videos. There are many such videos on undergraduate courses, such as elementary calculus, abstract algebra, ...
5
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1answer
157 views

Prerequisites for bredon's “Topology and Geometry”?

My background in topology is the first 6 chapters of Munkres's "topology" and in algebra Herstein's "topics in algebra". Both of them I self studied. A look at the table of contents of bredon's ...
5
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2answers
71 views

Mathematics lessons online?

IN school, I did not really care about my future, until I started working with computers, and getting into programming. I'm doing computer science at the moment & its currently really easy, but ...