Questions about studying mathematics without formal instruction.
6
votes
1answer
837 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 ...
3
votes
2answers
231 views
Factor groups and isomorphisms
I've somewhat recently been going back through one of my brother's old textbooks reviewing group theory. I'm up to a chapter called Factor-Group Computations and Simple Groups. The problems at the ...
0
votes
1answer
121 views
Course Dependency Checking for an Engineer
tl;dr : Is the dependency in the figure attached accurate?
Long Version : I am through with my engineering and am shifting to math for grad school. I am looking forward to re-learning (reviewing) ...
0
votes
1answer
874 views
Can “How to Prove It” replace Baby Rudin for me?
I am an engineer with tons of math courses behind me. However, all of them were applied wherein instead of giving us intuition, they gave us a toolbox. (If you encounter this then use that to solve.)
...
30
votes
3answers
2k views
Do you prove all theorems whilst studying?
When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
2
votes
2answers
73 views
Need help interpreting a passage from an old text on Diophantine equations
I need help interpreting this passage from page 35 of the book Diophantine Analysis by Robert D Carmichael.
"Thus the problem of solving Eq. (1) is reduced to that of solving Eq. (4) for $u$ and $v$ ...
1
vote
1answer
391 views
Help me find a book for self-study Calculus/Analysis
I read here all the recommendations but looking at tables of contents of each book none satisfies what I need.I am given a book series that has 4 volumes and 2800 pages but it is very hard to follow.I ...
1
vote
2answers
218 views
Stuck on rewriting logical implication
I've started to work through Applied Mathematics for Database Professionals and have been stuck on one of the exercises for two days. I've been able to prove the expression: $$\left( P\Rightarrow Q ...
5
votes
1answer
340 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 ...
10
votes
3answers
363 views
Should I look at syllabi for math courses before beginning my bachelor's degree in math?
Next year I'll start my bachelor's degree on mathematics, but I want to study something about it while I'm idle.
I've found this:
http://webdocs.registrar.fas.harvard.edu/courses/Mathematics.html
...
4
votes
2answers
139 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 ...
0
votes
1answer
228 views
Real Understanding definition/theorem, example for Linear Algebra
I have something to discuss about mathematical understanding, and use the Linear Algebra as example.
Sometimes, I feel the intuitive understanding of definitions/theorems itself is very different ...
0
votes
1answer
58 views
Derivation of rules pertaining to group $S_{3}$, from Artin's Algebra 2e
I'm reading Algebra 2e by Michael Artin. I'd be grateful for any guidance on 2 closely-related questions from Section 2.2, Groups and Subgroups, p. 42, excerpted below. First, I can understand the ...
11
votes
2answers
321 views
Computation of $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$
Can you please give some examples of computation of the derived functors $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$ for some simple cases, say $R=\mathbb{Z}$ or $R=\mathbb{Z}[G]$ for some ...
5
votes
2answers
787 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) ...
10
votes
2answers
299 views
Yoneda Lemma Exercises
Can you please suggest some (relatively simple) exercises to practice the use of the Yoneda Lemma? Harder exercises are welcome too, but I would like to start with simpler ones.
The answers to this ...
2
votes
2answers
361 views
Percent change over time
I have the following data:
$$\begin{array}{c|c|c}2010 & 2011 & 2012 \\\hline 50 & 20 & 30 \\\end{array}$$
How would the percent change be calculated?
Like this:
...
1
vote
0answers
245 views
How to enjoy doing what a mathematician does? [closed]
Reading a paper in which many formulas have been involved regardless the original concept is fairly a usual case happens to me often since the mathematics is the basics of anything. Sometime I enjoy ...
3
votes
1answer
142 views
Notation in linear algebra, what are $N(T)$ and $R(T)$
Working through some stuff I found on the web, I came across a notation that I haven't seen in my textbooks.
In this problem, $ T: P_4(\mathbb R)\rightarrow \mathbb R^4 $ is a linear transformation, ...
5
votes
2answers
1k 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 ...
5
votes
3answers
551 views
The most common theorems taught in Abstract Algebra
I am self learning abstract algebra. I want to know which theorems are a must to understand.
Now these are limits I have to deal with (please consider when answering):
I have limited ...
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 ...
0
votes
1answer
327 views
Good book to help me relearn Algebra 1…
In 8th grade I took Algebra 1 and did not learn a thing.I am now in Cal AB and making B's.
I was hoping to reteach myself Algebra 1 this summer by watching Khan Academy and reading a book on Algebra ...
1
vote
1answer
55 views
Resource to improve ability to interpret and understand formulas and algorithms
I wasn't sure whether this belonged here or on StackOverflow but here goes:
I've been doing a lot of research into algorithms recently and I've found that my inability to properly interpret and ...
3
votes
2answers
266 views
Linear algebra books that start with basic algebra?
I'm 30 years old, and the only math I can remember from college is basic algebra and some probabilities. Next month, I have a machine learning project I'd like to work on, but I'll need a solid ...
25
votes
1answer
425 views
How do I find partners for study?
I want to find partners to study some post-graduate topics together online (because I'm pretty much out of steam as far as self-study goes, and I have problems finding a decent grad school). Are there ...
1
vote
1answer
185 views
Undergraduate Research question
I've just finished my first analysis course, unfortunately I will not be able to continue studying as my family needs me to work for income. I was wondering if there is any meaningful research I can ...
0
votes
1answer
271 views
Is self-learning compatible with a college schooling? [closed]
I consider myself a self-learner, meaning: 1) I'd rather read a book or watch a video than sit through lectures and 2)I like having plenty of control over what I learn and how I learn it.
-
With ...
12
votes
4answers
717 views
Number of subgroups of prime order
I've been doing some exercises from my introductory algebra text and came across a problem which I reduced to proving that:
The number of distinct subgroups of prime order $p$ of a finite group ...
0
votes
0answers
162 views
Math books for ultra dummies
I'm searching for an applied math book (preferably applied to computer programming / 3D physics) which covers extensively every passage (complex calculations are just a bunch of semi-atomic operations ...
0
votes
2answers
88 views
Helping on how to improve in the online world [closed]
I had a bad Math teacher (really, terrible), and I also didn't imagine that was such a lovely world and in every thing we do, Math can be applied.
Plus I took the technical path in school (Industrial ...
5
votes
6answers
689 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 ...
3
votes
3answers
120 views
Problem based on Mapping of Functions.
A function $f:\mathbb{R}\to \mathbb{R}$ is define by, $$f(x) = \frac{\alpha x^2 + 6x - 8}{\alpha + 6x - 8x^2}$$Find the interval of values of $\alpha$ for which $f$ is onto.
So, here is what I ...
1
vote
0answers
165 views
Are Specific Facts about the Riemann Integral Logically Required?
This question is somewhat in the spirit of this one in that I am trying to understand the most efficient path to the major integral theorems (Fubini, change of variables, etc).
My question is this: ...
20
votes
3answers
597 views
When to skip sections of a book when self-studying?
When you're taking a mathematics class, you usually know exactly what sections of a book you need to know, and you can focus your time on these important sections.
However, when studying by myself, ...
5
votes
2answers
257 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, ...
3
votes
2answers
69 views
Problem based on Composite Functions.
Let $f(x) = \sin^{2}{x} + \sin^{2}\left(x + \frac{\pi}{3}\right) + \cos{x}\cos\left(x + \frac{\pi}{3}\right)$
and $g(x) = \left\{\begin{array}{rcc} 2x,\quad0\le x<1 \\x + \frac{1}{4},\quad 1 \le ...
5
votes
2answers
439 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 ...
3
votes
2answers
309 views
What's a good progression/path for self-educating from pre-algebra and beyond?
I never got very far in my math studies; I took zero math in college and had terrible teachers in high school. Fast forward to today and I'm a professional developer who's starting to feel that my ...
1
vote
1answer
227 views
Number theory for a high school Calculus student?
I've always loved playing with numbers, but haven't had any formal guidance in the study of advanced mathematics and number theory. Is there a book (or a few books) on mathematics that I wouldn't have ...
11
votes
3answers
1k views
Is memorization a good skill to learn or master mathematics?
I sometimes spend inordinate amounts of time memorizing math articles or theorems/proofs or formulas. My question is "am I wasting time?" and will 'active thinking' or 'working out problems' be faster ...
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 ...
0
votes
2answers
155 views
Practical Mathematics?
I am looking to brush up on my math skills so that I can use those skills when working with problems in machine learning, AI analyzing very large data sets. Most of the problems that I am likely to ...
0
votes
1answer
106 views
Advice for Area problem
I am very interested in a certain problem and I am wondering what methods currently exist to solve it. Given a curve defined by a function which maps any given arc length, s, from an arbitrarily ...
4
votes
2answers
1k 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 ...
28
votes
6answers
1k views
Attitude towards exercises in mathematics
I'm doing self study on a couple of topics in mathematics, such as real analysis, abstract algebra, and linear algebra. From time to time, there are always a couple of exercises which I found too ...
16
votes
6answers
1k views
Game theory - self study
I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
5
votes
1answer
165 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
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 ...
16
votes
7answers
2k views
How can I learn to “read maths” at a University level?
When I look at math, it's like my mind goes fuzzy.
The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
