Questions about studying mathematics without formal instruction.

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6
votes
4answers
262 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
3answers
589 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 ...
2
votes
3answers
457 views

Is there a problem in studying analysis before calculus?

Is there a problem in studying analysis before calculus? Most people say that analysis is rigorous calculus, the university I'm studying teaches calculus first because they believe it's better for the ...
4
votes
3answers
419 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 ...
10
votes
9answers
633 views

Suggest an Antique Math Book worth reading?

I'm not a math wizard, but I recently started reading through a few math books to prepare myself for some upcoming classes and I'm starting to really get into it. Then I noticed a few antique math ...
0
votes
2answers
400 views

If $p_1 = 0.3$ and $p_2 = 0.4$, what is the probability that it will take Jay more than 12 hours to be successful on both jobs?

Jay has two jobs to do, one after the other. Each attempt at job $i$ takes one hour and is successful with probability $p_i$. If $p_1 = 0.3$ and $p_2 = 0.4$, what is the probability that it will take ...
1
vote
4answers
71 views

Measure nonzero implies dense on a rectangle

This would be a very handy lemma for me but I have been unable to prove it thus far. If $S \in \mathbb{R}^n$ is bounded and is not of measure zero, then there exists a rectangle $R$ such that $S$ ...
3
votes
2answers
1k views

An ambulance problem involve sum of two independent uniform random variables

An ambulance travels back and forth at a constant speed along a road of length $L$. At a certain moment of time, an accident occurs at a point uniformly distributed on the road.[That is, the distance ...
4
votes
0answers
188 views

How does one study with many textbooks?

Suppose you wanted a good understanding of a subject, and so you start reading a recommended textbook. But it turns out that the textbook you have has a different perspective/omits certain topics, ...
9
votes
3answers
324 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 ...
0
votes
3answers
57 views

Independent random variables $Y_i$ with $Y_i \sim N(0,\sigma^2)$

I am struggeling with this problem: How to show that, $E(Y^2 _i /σ^2) = 1$ I tried: $$E(Y^2 _i /σ^2)=E(Y^2 _i /(Y_i - \bar{Y})^2) = E(Y^2 _i /(Y^2 _i - 2Y_i\bar{Y} + \bar{Y}))=...$$ However, I am ...
25
votes
5answers
847 views

What's the best way to measure mathematical ability?

Very soft question I admit, but it's something that's been bothering me for a while. I've been thinking that being self taught has the problem of accreditation. You can't evaluate a mathematician ...
1
vote
2answers
300 views

How to effectively calculate $(1/\sqrt1 + \sqrt2) + (1/\sqrt2 + \sqrt3) +\cdots + (1/\sqrt{99} + \sqrt{100})$ [duplicate]

I have this series: $$\frac{1}{\sqrt1 + \sqrt2} +\frac{1}{\sqrt2 + \sqrt3} +\frac{1}{\sqrt3 + \sqrt4} +\cdots+\frac{1}{\sqrt{99} + \sqrt{100}} $$ My question is, what approach would you use to ...
1
vote
3answers
651 views

What are the best websites for learning math? [closed]

What I known: this site mathoverflow khanacademy Are there any other website for learning math? Which one do you think is the best?
2
votes
2answers
142 views

The shape of mathematical self-tutelage

I am interested primarily in physics, and I am generally self-taught in mathematics. However, this implies an inaptitude for rigorous proof. While I am confident that I can grasp the concepts and ...
1
vote
1answer
173 views

Selecting Differential Geometry Exercises

I'm self-studying differential geometry with Do Carmo's books "Differential Geometry of Curves and Surfaces" and "Riemannian Geometry" and I find those books very good, however I feel a little ...
20
votes
2answers
512 views

Do free online collaborative solution manuals exist?

I'm not a mathematician by training and a rarely come in contact with mathematicians. For this reason I find solution manuals to be incredibly useful - reading them allows me to see how experienced ...
1
vote
1answer
363 views

Why “hinge” loss is equivalent to 0-1 loss in SVM?

I'm reading a book named The Elements of Statistical Learning by Hastie et al. In $\S 12.3.2$ it introduced the SVM as a penalization method: With $f(x)=h(x)^T \beta+\beta_0 $, the solution of the ...
4
votes
1answer
263 views

Looking for a logically coherent book for the self-study of differential equations

I'm looking for a logically coherent book for the self-study of differential equations. Let me clarify. By logically coherent, I don't mean proofs of the limit laws, uniqueness theorems etc. By ...
0
votes
2answers
98 views

Finding the stationary point on the curve: $e^x+ye^{-x}=2e^2$

So I'm trying to find the stationary point of this equation: $e^x+ye^{-x}=2e^2$. This is my attempt at doing so: $$\dfrac{d}{dx}(e^x+ye^{-x})=\dfrac{d}{dx}(2e^2)$$ $$e^x+(-ye^{-x}+\frac{dy}{dx}\times ...
8
votes
7answers
4k 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" ...
5
votes
0answers
139 views

The high road to learn algebraic geometry

Suppose that a student has a basic knowledge in commmutative algebra at the level of the Atiyah-MacDonald. What do you think about the following steps to learn algebraic geometry? step 1: read ...
3
votes
1answer
500 views

Is “Functional Analysis” by “Yosida” a good book for self study?

I was wishing to start studying by myself the book Functional Analysis by Yosida, does anyone have already used it, is it a good reference?
2
votes
1answer
290 views

As an Introduction - A Mathematical Introduction to Logic by Herbert B. Enderton?

I am attempting to study logic by myself. I acquired the book A Mathematical Introduction to Logic by Herbert B. Enderton. I want to ensure that this is a good introduction so, is this a good ...
3
votes
1answer
137 views

Formality fades away in the air

I'm trying to study by myself mathematics, but I realized that I have only a naive notion of certains building blocks of mathematics; certain parts of the formalism. So I tried to start with logic, ...
3
votes
2answers
89 views

Please, help me to find where is a mistake in the solutions of the equation.

I have this equation and I will be very thankful to anyone who can provide me any help with the one discrepancy in my solution and the solution from the self-learning website: $$ \frac{1+\tan(x) + ...
6
votes
1answer
393 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 ...
4
votes
2answers
143 views

How many ways to visit 6 cities twice without visiting the same city twice in a row?

A person wishes to visit 6 cities, each exactly twice, and never visiting the same city twice in a row. In how many ways can this be done? I tried complement. Define $S(n)$ as the number of ...
6
votes
2answers
287 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 ...
9
votes
7answers
460 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 ...
29
votes
8answers
1k views

How to use math textbooks

I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it. I have run into a ...
3
votes
7answers
431 views

What fields of math would be most interesting for non-mathematicians?

I'm a regular high schooler with an interest in mathematics, but I don't think I will study (pure) mathematics in university, because I'm leaning slightly more towards aerospace engineering and/or ...
1
vote
3answers
365 views

Where to pick up learning math again?

In high school, I absolutely loved math classes. I took Calc in 11th grade, and then since have done just about nothing with math. Is there somewhere I go to see what math knowledge I still ...
2
votes
3answers
114 views

Lebesgue covering theorem

I am having trouble understanding Lebesgue covering theorem as stated in Mathematical Encyclopedia. First of all I think I have confusion with the definition of "finite subsystem". Is it finite ...
6
votes
1answer
229 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. ...
20
votes
3answers
3k views

I want to get good at math, any good book suggestions?

I have never been good at math. In my senior year I failed algebra 2 in the first semester because the teacher would refuse to show me how to solve problems saying that it's my fault for not paying ...
44
votes
6answers
4k views

Studying for the Putnam Exam

This is a question about studying for the Putnam examination (and, secondarily, other high-difficulty proof-based math competitions like the IMO). It is not about the history of the competition, the ...
4
votes
1answer
107 views

Is it allowed to divide an equation by an expression which can be equal to zero?

I need a help in such a problem and will greatly appreciate any suggestions. I was taught, division of an equation by an expression which can be equal to zero can lead to missing roots. But I thought ...
1
vote
3answers
896 views

Resources for self-study of general topology

Could you point me to good resources for self-study of general topology. I want to learn the basics and how to prove theorems about structures like polyhedra by myself.
2
votes
2answers
95 views

Recommended topics for Chemical Engineering grad.

I'm a Chem. Eng. grad. I did well in my math courses and I really like math. I've started digging for some more to learn on my own. I like applying math but I'm most satisfied when I have a deep ...
113
votes
6answers
4k views

Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
4
votes
1answer
163 views

Hard time delivering other than algebraic proofs

I'm enrolled in some different math (related) courses thought by the CS department at a university (although I'm unable to attend most of the classes due to work). Even though the focus of these ...
9
votes
3answers
310 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 ...
6
votes
2answers
555 views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
1
vote
2answers
130 views

What course sequence should I study in order to build a foundation for studying cryptography and signal processing?

I studied mathematics about two decades ago, but unfortunately, I remember little of it. I'm hoping to start studying cryptography and signal processing, but I'm not entirely sure what ...
11
votes
3answers
181 views

Transitioning to Elementary School teaching and need some advice on bolstering my math skills

I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
6
votes
2answers
106 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)\\\\ ...
4
votes
2answers
388 views

Where to go after Advanced Calculus 2?

I will be finishing up Advanced Calculus 2 soon and I would like to continue self studying Analysis. I want to learn Real and Complex Analysis, Measure Theory and all that other good stuff. but I am ...
2
votes
2answers
350 views

Books for algebraic geometry, algebraic topology [duplicate]

Possible Duplicate: (undergraduate) Algebraic Geometry Textbook Recomendations I am planning to self-study one of these two subjects: Algebraic geometry , Algebraic topology. I can borrow ...
0
votes
3answers
527 views

Books for Self learning math from the ground up

I am a CSE graduate currently working as a .NET and android developer. I feel my poor basic in mathematics is hampering my improvements as a programmer. I want to achieve a sound understanding on the ...