Questions about studying mathematics without formal instruction.

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How to prove $\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b} <2$ [duplicate]

Prove the inequality for a triangle with sides $a,b,c$ we have $$\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b} <2$$ Trial: Since $a,b,c$ are sides of a triangle I know $a+b>c,b+c>a,a+c>b$ ...
6
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2answers
126 views

Independence of sigma-algebras

Good day to everyone. While solving some problem of studying character I obtained some statement to prove, which is like following (this is my internal interest to prove it rigorously). Assume that ...
6
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2answers
531 views

Does anyone know of any good ways to get good at algebra without as much“grind” as doing hundreds of questions a night

I'm coming to a point in college where I can't avoid my math classes any longer. I need to get better at algebra so I don't flunk out of the class when I take it, however I've never been able to get ...
6
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2answers
154 views

Is it a problem being unable to understand a mathematical definition without examples?

I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning ...
6
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2answers
765 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 ...
6
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2answers
119 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
1answer
187 views

How much Differential Geometry is needed to appreciate Algebraic Geometry?

I want to start self-studying Algebraic Geometry at some point in the near future. There are plenty of posts discussing prerequisites, but one thing I couldn't find a discussion of: How much ...
6
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2answers
335 views

Which books to study category theory?

I am an amateur math researcher in the field of general topology. I've set the purpose to learn enough category theory for my research. After reading Steve Awodey, "Category Theory", 2010, is it ...
6
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2answers
3k views

Some basic practical applications of Calculus

I am currently studying Calculus on my own for fun. I enjoy different components of math and how they can be used to solve so many problems. Many people, however, think I am crazy because I am ...
6
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2answers
369 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 ...
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1answer
412 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 ...
6
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1answer
738 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 ...
6
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1answer
212 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
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1answer
143 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 ...
6
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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
249 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 ...
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1answer
556 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. ...
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1answer
291 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. ...
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4answers
771 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 ...
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0answers
124 views

Finitely additive function on an infinite set, s.t., $m(A)=0$ for any finite set and $m(X)=1$ (constructive approach)

Other exercise which I found in Dudley's Analysis book: Show that there is a measure on a infinite set $X$, defined on $2^X$ s.t. is finitely additive, $m(A)=0$ for any finite set and $m(X)=1$. ...
6
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2answers
259 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
100 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
161 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
159 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 ...
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9answers
974 views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
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7answers
448 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
214 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 ...
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4answers
264 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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4answers
300 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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1answer
176 views

indefinite integral $\int\sin\sqrt[3]{x}~dx$

I want to determinate the integral $\int\sin\sqrt[3]{x}~dx$ . I tried to use integration by partitions and integration by substitution but I came to no result. I know the result which is shown here ...
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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6answers
80 views

What is the value of $a+b+c$?

What is the value of $a+b+c$? if $$a^4+b^4+c^4=32$$ $$a^5+b^5+c^5=186$$ $$a^6+b^6+c^6=803$$ How to approach this kind of problem. Any help. UPDATE: Thank you all for answers. Now I ...
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7answers
695 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 ...
5
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3answers
254 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
190 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 ...
5
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5answers
282 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 ...
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4answers
2k views

Learning trigonometry on my own.

I have been self teaching myself math beginning with a grade 10 level for a while now and need learn trigonometry from near scratch. I am seeking both books and perhaps lectures on trigonometry and ...
5
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1answer
155 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
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4answers
689 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
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1answer
200 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
175 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
139 views

Algebra and skills needed for Hatcher

A couple of months ago I asked a professor by e-mail to mentor me on topology during the summer. He advised me to study general topology (Hausdorff spaces, connectedness, compactness) and algebraic ...
5
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2answers
227 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 ...
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1answer
1k views

Can I go through Hartshorne without knowing much analysis?

I know intro abstract algebra and some real analysis. Is this enough to study algebraic geometry from the book of Hartshorne?
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 ...
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7answers
1k 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 ...
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2answers
384 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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1answer
799 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?
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5answers
957 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 ...