Questions about studying mathematics without formal instruction.
9
votes
5answers
4k views
Good abstract algebra books for self study
Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, ...
9
votes
7answers
490 views
Simple fact on linear operators
The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study.
We are given a linear operator $T$ over a finite dimensional vector space $V$. We have to show that $T$ is a ...
9
votes
5answers
320 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 ...
9
votes
1answer
890 views
How to self study Linear Algebra
I have no idea if this question is appropriate for this forum, but I hope you guys can overlook the fact that I asked it on a wrong forum (if I did) and still help me answer it (of course, if this is ...
9
votes
3answers
244 views
Doing maths without background knowledge
My mathematics work is proceeding beyond my wildest hopes, and I am
even a bit worried - if it's only in prison that I work so well, will
I have to arrange to spend two or three months locked ...
9
votes
3answers
190 views
Being ready to study calculus
Some background: I have a degree in computer science, but the math was limited and this was 10 years ago. High school was way before that. A year ago I relearnt algebra (factoring, solving linear ...
9
votes
3answers
498 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 ...
9
votes
1answer
699 views
Good introductory books on homological algebra
Which books would you recommend, for self-studying homological algebra, to a beginning graduate (or advanced undergraduate) student who has background in ring theory, modules, basic commutative ...
9
votes
2answers
386 views
Is Mathematics graduation important for a Computer Scientist?
I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all.
I am going to graduate in Computer Science in ...
8
votes
6answers
294 views
Making up for wasted high school years - where should I begin?
I realize this question is long and quite personal but any help will be greatly appreciated.
I'm a senior high school student. I've learnt maths at precalculus level. I have had little exposure to ...
8
votes
5answers
3k views
In what order should the following areas of mathematics be learned?
I am in a biological field (medicine) but I have genuine passion for mathematics. I want to learn it on my own , in my spare time. Mathematics , as I gather, is learned best when you have grasped ...
8
votes
1answer
343 views
Undergrad Student Trying to Figure Out What to Study
this is my first time on stack exchange and I am seeking advice for my future studies.
Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
8
votes
2answers
384 views
Question about all the homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$
An exercise in "A first course in Abstract Algebra" asked the following:
Describe all ring homomorphisms from the ring $\mathbb{Z},+,\cdot$ to itself.
I observed that for any such ring homomorphism ...
8
votes
2answers
138 views
Given $N$, count $\{(m,n) \mid 0\leq m<N, 0\leq n<N, m\text{ and } n \text{ relatively prime}\}$
I'm confused at exercise 4.49 on page 149 from the book "Concrete Mathematics: A Foundation for Computer Science":
Let $R(N)$ be the number of pairs of integers $(m,n)$ such that $0\leq m < N$, ...
7
votes
2answers
908 views
Path to Basics in Algebraic Geometry from HS Algebra and Calculus?
In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
7
votes
8answers
843 views
Self-study resources for basic probability?
I am taking a Computer Science class soon that requires a solid knowledge of the basics of probability. I've only had minimal exposure to probability in classes I've taken in the past, so I need to ...
7
votes
2answers
279 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
2answers
180 views
What kind of math topics exist?
What kind of math topics exist?
The question says everything I want to know, but for more details: I enjoy studying mathematics but the problem is that I can't find any information with a summary ...
7
votes
2answers
468 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
2answers
50 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
386 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
5answers
250 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
2answers
1k views
Is Aluffi's book a good second text for Algebra?
I have been trying to relearn parts of algebra (mostly module theory and (advanced)linear algebra) from Lang, which, frankly, is not going too well.
Now, I have managed to get my hands on 'Aluffi - ...
7
votes
2answers
200 views
The role of writing in understanding concepts
I am an engineer student from Norway who is not that fascinated with "engineering maths", so I am trying to work through Spivak's Calculus book on my own. I know that there is no "how to" manual for ...
7
votes
2answers
420 views
Math route for someone of this background
Apologies for a soft question. I do not have a lot of time because of my job (programmer) and my wife cannot work so I cannot quit. I also did not graduate from a very prestigious school with good ...
7
votes
1answer
122 views
How to improve mathematical creativity?
To introduce myself: I'm an undergraduate mathematics student in Germany. Currently I'm studying in the second semester and until now I'm doing well, but I still got the feeling that my ability to ...
7
votes
1answer
753 views
Tips for an adult to learn math — from the beginning.
First let me start with I am an adult and I can't do simple maths. I some how got through all of my math courses in University (after several attempts) but I honestly couldn't tell you how...
I ...
7
votes
1answer
335 views
Automatizing computational skills
"It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise ...
6
votes
5answers
795 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 ...
6
votes
5answers
354 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
5answers
811 views
Advice for benefits to directly use analysis textbook to replace calculus
Main purpose: For self-learning performance, neither for exam nor degree courses.
Calculus textbook using now[1]: Calculus I, Weinstein&Marsden, UTM, Springer
Question Description: I've been ...
6
votes
5answers
2k views
Which calculus text should I use for self-study?
I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
6
votes
3answers
106 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
2answers
267 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 ...
6
votes
2answers
412 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 ...
6
votes
3answers
385 views
How to deal with the temporary nature of my knowledge?
I'm a self-learner trying to learn Math while enrolled in a wrong major (Humanities). I have gone through the many amazing questions and answers here (& elsewhere, including Prof. Tao's blogs) ...
6
votes
5answers
283 views
Calculus book recommendations (for complete beginner)
Well I have not started calculus yet but I am really keen to.
I would love if you suggest some books.
Points to be noted:
I really don't like the way textbooks are written so please no "textbooks"
...
6
votes
2answers
72 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
4answers
177 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
164 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
833 views
How do I get good at Math?
How do I get good at math?
I'm a freshman in college, and I've always done OK in math. I never had any good teachers in High school, and I always have done the bare minimum. Over the course of this ...
6
votes
1answer
437 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
4answers
327 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
votes
0answers
104 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 ...
6
votes
0answers
479 views
Efficient ways to read and learn a new topic
I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
6
votes
0answers
580 views
Which is better strategy to learn and read books, traditionally one by one OR re-read carefully on perfect books
(Just focus on how to learn and master the stuff pretty well, not involve the aspect of courses or exam)
Because recently I always feel that the time and energy are pretty limited, I want to try ...
5
votes
6answers
688 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 ...
5
votes
5answers
765 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.
5
votes
3answers
502 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 ...
5
votes
4answers
394 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 ...
