Questions about studying mathematics without formal instruction.

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2
votes
1answer
130 views

Recurrence relation: $T(n) = T(n-1) + 1/n$

\begin{align} T(0) & = 0 \\ T(n) & = T(n-1) + \dfrac{1}{n} \end{align} solve the recurrence relation My work so far: \begin{align} T(1) & = 1 \\ T(2) & = 1 + \dfrac{1}{2} \\ T(3) ...
7
votes
5answers
1k 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 ...
6
votes
3answers
250 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 ...
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. ...
13
votes
5answers
1k views

Book on the Rigorous Foundations of Mathematics- Logic and Set Theory

I am asking for a book that develops the foundations of mathematics, up to the basic analysis (functions, real numbers etc.) in a very rigorous way, similar to Hilbert's program. Having read this ...
3
votes
1answer
206 views

Problem Regarding Time Management

I don’t know whether it’s the right place to ask for such a request. I would like to express my apologies in advance if it anyhow goes against the dignity of the forum. I’m taking preparation for a ...
4
votes
8answers
970 views

Studying Math, All Over Again

I am 16 and never really paid attention to math. For me it was just one more obstacle in passing the exams. Now that I study computers, mostly on my own, I find that there is indeed a need for me to ...
3
votes
2answers
88 views

Confusion on Eigenvalues of Similar Matrices

Please help me to identify where I went wrong: The completely reduced normal form of the real matrix $A= $\begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ ...
8
votes
2answers
419 views

Strengthening My Foundation in Mathematics

"For every equation you introduce, you cut your audience in half." This expression, which I believe came from Stephen Hawking, summarizes why I believe that I have a weak foundation in ...
1
vote
1answer
110 views

Non-constant entire function

Does there exist a non-constant entire function $f$ which is constant for $|z|<1?$
2
votes
3answers
78 views

easy activity to train finding pattern ability?

I realize that my math learning go wrong way. Wikipedia says math is finding pattern, formulating conjectures, and proving it. but my math learning didn't focus on them. memorizing formula doesn't ...
2
votes
1answer
238 views

How to improve Maths skills after a physics degree.

A few years ago finished a physics degree and one of the biggest lessons I learned is that I need to spend some extra time on pure Maths. In fact I almost wish I done a maths degree first as that ...
2
votes
3answers
60 views

Differentiation; trouble finding $\frac{dy}{dx}$ in terms of $y$

I'm self-studying through some exercises on differentiation, and have found a section which I've gotten almost every question wrong. Can anyone help me find out where I'm going wrong? An example of ...
5
votes
2answers
501 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 ...
2
votes
1answer
148 views

Easy papers on fundamental groups (for beginners)

I'd like to read some papers concerning fundamental groups, for example, papers written to explain some basic facts about homotopy explicitly for undergraduate students. All the papers I have ...
10
votes
5answers
606 views

Notes for Beginner Fourier Analysis?

Are there any good lecture notes or books on basic fourier analysis that authors publish freely online? It is very difficult to find rigorous mathematical theory of fourier analysis because google is ...
3
votes
2answers
327 views

Universal arrows' definition

I'm having trouble understanding the definition of a universal arrow in Maclane's CWM. In particular, what are the fixed arguments? I know at least the functor is fixed, but I can't tell if $c$ is ...
4
votes
2answers
464 views

Follow-up to Baby Rudin

I would like to continue my study of analysis, albeit temporarily in self-study, and I was wondering what would be the best "sequel" to baby Rudin. Thank you very much for your advice.
1
vote
1answer
205 views

Sternberg's Advanced Calculus [closed]

I have taken an analysis course using baby Rudin as the text, and I would like to keep up by analysis skills while developing on them. As such, I want to work through Sternberg's Advanced Calculus on ...
2
votes
1answer
595 views

Complete course for self-study!!!

I'm the second-year college student in the Mathematics Faculty. I'm having difficulty in finding orientation for self-study. Can anyone show me the course of Mathematics in some universities in the ...
2
votes
5answers
130 views

What am I doing wrong in calculating this determinant?

I have matrix: $$ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 3 & 3 & 3 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \end{bmatrix} $$ And I want to calculate ...
3
votes
1answer
461 views

Relearn mathematics

I believe that this question is well known, but since I'm not a US resident and do wish to learn math according to the U.S. school syllabus I wish that somebody can help me. At my first eight years ...
3
votes
1answer
201 views

Hom-functor (Bifunctor)

I'm having trouble seeing how just by having the (co- and contravariant) functors $Hom(a,-)\rightarrow Set$ $Hom(-,b)\rightarrow Set$ I can define the bifunctor $F:C\times C\rightarrow Set$. ...
3
votes
2answers
269 views

Require brilliant resources to self teach.

I'm far from the level of mathematical knowledge every user on this website posseses, however I am very much determined to get there as my love for mathematics increases. These are the topics: ...
1
vote
0answers
296 views

Learning Functional analysis in one month.

Background: Master in Engineering, applied physics. Now: New phd student in applied math. Goal: Pass functional analysis with good grades. I have not had so much time for studies period since there ...
15
votes
1answer
709 views

Learning path to the proof of the Weil Conjectures and étale topology

Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" ...
27
votes
8answers
3k views

Math every mathematician should know [closed]

Sorry in advance if this question doesn't belong here. I know it walks the line of what kinds of questions should be asked, but I'm really interested in what the community here has to say on it. ...
11
votes
8answers
2k views

A Book for abstract Algebra

I am self learning abstract algebra. I am using the book Algebra by Serge Lang. The book has different definitions for some algebraic structures. (For example, according to that book rings are defined ...
2
votes
3answers
506 views

Suggestions on Real, Fourier Analysis textbooks?

I'm new here, and I hope this is within the scope of the website. I'll try to ask few advisory type questions in the future... I'm a college junior, and I was wondering if you guys could offer any ...
14
votes
3answers
690 views

Careers in Math

I am a highschool freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of ...
3
votes
1answer
174 views

Reading circle in mathematics?

How to learn about interesting topics in a small group of people?It seems very useful to broaden your mathematical background and get to know topics that are away from your field of specialization. ...
143
votes
27answers
12k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
2
votes
1answer
107 views

The opposite functor

Given a functor $F : A \rightarrow B$, I managed to define the functor $F^{op} : A^{op} \rightarrow B^{op}$. Now, I cannot see how to use it to define a functor from and to $\text{Cat}$ such that $C ...
1
vote
4answers
162 views

Opposite category functor

I need some confirmation: is the opposite category transformation always a functor? Also, isn't it always the case that $C^{\text{op}} = C$, since the the way we label an arrow does not matter?
3
votes
1answer
274 views

A High-School Freshman's Journey Into Calculus

The short version: What path should I take to learn Calculus in High-School? The long version: I am a high-school freshman, and I am enamored with mathematics, and I just see beauty in many things ...
1
vote
0answers
184 views

A rigorous book (or preferrably set of notes) on classic multivariable calculus-analysis?

This is different to (Theoretical) Multivariable Calculus Textbooks as I want a classical treatment of line and surface integrals without the notion of a differential form. Prerequisites: Paths, ...
2
votes
1answer
179 views

Doubt - Proof of completeness of number system [duplicate]

Possible Duplicate: Choice of $q$ in Baby Rudin’s Example 1.1 I am going through Walter S. Rudin - Introduction to Mathematical Analysis,3rd Edition. In his proof of the existence of real ...
1
vote
1answer
4k views

What is the standard form of a linear programming (LP) problem?

According to Bertsimas' text, the standard form of a LP problem is: According to Vanderbei's text, the standard form of a LP problem is: So, what is the standard form of a linear programming ...
18
votes
6answers
3k views

Self-Studying Abstract Algebra; Aye or Nay?

I am a high schooler with a deep interest in mathematics, which is why I have self-studied Linear Algebra and have begun my self-study in Differential Equations. As I am a man who likes to plan ahead, ...
1
vote
1answer
364 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
1
vote
4answers
210 views

Which books /tutorials will be good for these topics for AI computer science student

I have found from the internet that I need to know these topics for understanding Artificial Intelligence: Matrix algebra: most machine learning models are represented as matrices and vectors. ...
0
votes
1answer
220 views

Linear programming / linear optimization with R? [closed]

Any good books or websites that teach linear programming / linear optimization with R? Thanks. Edit (Jan 6, 2013): The following R code is an example by using the "lpSolve" package. ...
0
votes
2answers
937 views

Can you suggest me a good book for self-study of analytic geometry 1?

I'm stuyding mathematics alone, but I plan to enter in the university in the near future, I went to the university website and it suggests Analytic Geometry 1 as part of their curricula, the topics ...
3
votes
2answers
430 views

Algebra book(s): Beginner through to advanced

I admit, I am not great at Maths; I'm situated in one off the lowest Maths class for my year, partly due to myself losing focus last year. Though, I like maths, I really do. Especially since I do a ...
6
votes
4answers
1k views

Are there any memorization techniques that exist for math students?

I just watched this video on Ted.com entitled: Joshua Foer: Feats of memory anyone can do and it got me thinking about memory from a programmers perspective, and since programming and mathematics ...
1
vote
2answers
215 views

Need advice. How relearn what Ive forgotten?

The last time I studied mathematics and algebra was six years ago. I've since forgotten everything except quadratic equations, trigonometric functions and other things at the same level. Now I want to ...
12
votes
3answers
784 views

What should a math graduate know? [closed]

There are a lot of undergraduate courses out there and most of them agree on certain things, with regard to the subjects covered. Courses that include mathematics (engineering, physics, etc) are ...
0
votes
1answer
124 views

Integrate $\int \frac{1}{x^3}e^{-x^2}dx$

$$\int \frac{1}{x^3}e^{-x^2}dx$$ What I did? put $1/x^2 = t; $ then $\int \frac{1}{x^3}e^{-x^2}dx$ will trasform into $\frac{-1}{2}\int e^{-1/t}dt$ I don't understand how to proceed there after. ...
16
votes
3answers
920 views

What is the prerequisite knowledge for learning Godel's incompleteness theorem

I am very interested in learning the incompleteness theorem and its proof. But first I must know what things I need to learn first. My current knowledge consists of basic high school education and the ...
1
vote
1answer
197 views

GCD to Linear Diophantine Equation without Euclid Algorithm

Is there a technique other than performing Euclid's algorithm in reverse that can elegantly show that if GCD$(a,b) = d$ then there exist integers $x$ and $y$ such that $ax + by = d$?