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2
votes
2answers
227 views

Is it mathematically wrong to prove the Intermediate Value Theorem informally?

I have been looking at various proofs of the IVT, and, perhaps the simplest I have encountered makes use of the Completeness Axiom for real numbers and Bolzano's Theorem, which, honestly, I find a bit ...
2
votes
0answers
44 views

How long before the prey can escape?

I've (sort of) come across the following problem in my research. The actual scenario is a little abstract to explain, so I'm rephrasing the problem in terms of a predator/prey scenario. I'm tagging ...
6
votes
1answer
258 views

Please recommend good text on complex Fourier series/analysis

I am looking for some good text/reference on complex Fourier series resp. Fourier analysis for complex (in particular holomoprhic) functions (of one variable). The more it contains on this particular ...
0
votes
1answer
47 views

Probability as a function of time

I was really wondering when I have to select any one out of the n options available - the probability of selecting A (let's say) is 1/n. But then I'm confused. When I (or anyone/anything else) bring ...
2
votes
3answers
56 views

How do set theory, and formal logic fit in together?

Im at that stage in my mathematical understanding where I kinda understand what set theory is and what first order logic is but dont really understand how they fit together to create Mathematics. I ...
1
vote
1answer
57 views

what is significant about closed sets? [on hold]

Looking at this, what is the Significance / usefulness of a set being closed? what more can be deduced when a set is proved to be closed ? l am sure it activates number of short cuts in proving ...
2
votes
1answer
69 views

What's a good book on geometry to read after Kiselev?

I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so. Which book would you suggest that one may read after finishing Kiselev?
1
vote
1answer
38 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
5
votes
7answers
743 views

Supplementary reading for probability theory studies

Can you advise some good books covering areas which are required for serious probability theory studies (e.g. measure theory, functional analysis)? Preferably this book should have some problem sets ...
51
votes
5answers
10k views

How Do You Go About Learning Mathematics?

I really like mathematics, but I am not good at learning it. I find it takes me a long time to absorb new material by reading on my own and I haven't found a formula that works for me. I am hoping a ...
12
votes
2answers
763 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 ...
36
votes
2answers
786 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 ...
26
votes
3answers
985 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, ...
15
votes
3answers
1k 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 ...
18
votes
5answers
5k 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 ...
34
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 ...
8
votes
2answers
228 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 ...
31
votes
8answers
5k 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 ...
9
votes
2answers
4k views

How to improve mathematics for Programming Contests?

You might close this question or vote "-1" for this but I just can't stop myself from asking this question from the experts of mathematics which solves thousands of problem related to mathematics and ...
8
votes
2answers
684 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?)
53
votes
17answers
31k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
5
votes
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?
3
votes
1answer
525 views

Making theorems into flashcards?

I am studying real analysis and trying to convert some of the rather wordy theorems into flashcards. Some of the theorems have names and so it's easy to make a flashcard that just asks that I state ...
6
votes
5answers
881 views

Materials for self-study (problems and answers)

I'm hoping to self-study Geometry, Algebra, Calculus, Vector Calculus, Linear Algebra, Probability and Statistics, and other intermediate maths. I've found the best way for me to learn is to work on ...
12
votes
2answers
991 views

Math Notes and Knowledge Organization Methodology

I, like many of you I suspect, take copious notes when reading and working through math exercises/theorems/constructions. I have stacks and stacks of notes ranging from one day old to several years. ...
16
votes
4answers
3k views

Can I use Ravi Vakil's way of learning for elementary subjects?

I mean you can't learn math in a linear order. Can I just read a paper first on a subject I haven't studied and just work backwards? For example, I have never studied combinatorics but I sort of have ...
70
votes
6answers
6k views

Strategies for Effective Self-Study

I have a long-term goal of acquiring graduate-level knowledge in Analysis, Algebra and Geometry/Topology. Once that is achieved, I am interested in applying this knowledge to both pure and applied ...
14
votes
4answers
620 views

Recommended Math knowledge for programming

I wasn't sure if this is a math or programming question so I suppose I flipped a coin. I'm just learning programming thanks to my IT Support degree and was just wondering what the minimum recommended ...
120
votes
20answers
8k views

Are there any open mathematical puzzles?

Are there any (mathematical) puzzles that are still unresolved? I only mean questions that are accessible to and understandable by the complete layman and which have not been solved, despite serious ...
9
votes
2answers
578 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 ...
4
votes
3answers
896 views

Suggest me the path to learn Maths

I am a Software Engineer. With interest on computers I have chosen this path. But I don't know anything about great maths. I want to learn from basic to some level(which would help me in my ...
3
votes
5answers
784 views

Preparing for first year CS

I'm in Italian guy almost in my 30. I have a regular job as a programmer. When in school I've never been much interested nor good in math and even at the university I've been studying languages, hence ...
0
votes
0answers
61 views

Engelking or Munkres for General Topology? [on hold]

I am a last-year Bachelors student and when I finish my Bachelors, I will have one year free time just before I start Masters in Pure Mathematics. I like to be better in General Topology before ...
1
vote
0answers
38 views

Possible Connections between Harmonic Analysis, Potential Theory and Analytic Capacity for a Fourier Analyst

So, Folks, here's the deal: After looking at this question, posted a little earlier on this site, and getting quite inspired by the beauty of this kind of result, I have got quite interested on this ...
10
votes
1answer
2k views

Using distance formula to find slope, any reason to use the concluding equation?

So, today I was observing a class that I will be a TA for this semester and the professor started to talk about the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Well, my mind wandered a little ...
12
votes
5answers
823 views

What are special functions for?

If you read enough mathematics, you eventually come across several so-called "special functions". I'm always left wondering what on Earth these things are actually for. We have the Euler Gamma ...
13
votes
4answers
1k views

Guidelines for learning about Ramanujan's work?

It is well known that one of the first books Ramanujan studied was "Synopsis of Pure and Applied Mathematics" and that it shaped the way Ramanujan thought and wrote about mathematics. Being interested ...
6
votes
1answer
78 views

How to get to the heart of a subject?

(mathematical subject is intended) It's obviously not a simple question, but I thought it could lead to some interesting discussion. I was reading Lewis Campbell's biography of James Clerk Maxwell ...
5
votes
7answers
1k views

How many ways are there to define sine and cosine?

Sometimes there are many ways to define a mathematical concept, for example the natural base logarithm. How about sine and cosine? Thanks.
1
vote
1answer
30 views

research in special function with Lie algebra

First of all, I don't know if this is the right place to ask about this. If not, please direct me somewhere I can get more help. I have to research in the field of special functions with a lie ...
4
votes
1answer
37 views

Mathematics of Magic Squares

I have seen many popular accounts of simple magic squares but I would like to find a proper mathematical background to understanding magic squares. What background knowledge do I need. I am a retired ...
1
vote
1answer
49 views

What are some genuine ways to define the derivative of a fractal?

Seeing the success of applying measure theory to generalize integration to fractals, I wonder whether or not there is a method to generalize the derivative to a fractal. Most courses start off fractal ...
2
votes
2answers
84 views

Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$ [duplicate]

I know that $\lim_{x\to0}\frac{x}{x}=$ 1. But in my text book, it is written that it is $\infty$ and even $\frac10=\infty$. But how is it possible? And are they both same? What is the difference ...
11
votes
3answers
749 views

Differentiable at a point

My roommates and I have an argument you guys can help to settle (peace is at stake, don't let us down!) In undergrad calculus courses, one usually explains what it means for a function to be ...
56
votes
13answers
4k views

Are all mathematicians human calculators?

I asked my dad why he did not major in math he said "because he is not good at math". I think I like math, and I think I'm ok at it, but I'm not gifted or anything like that, I just like math. I think ...
3
votes
4answers
3k views

What are some good Fourier analysis books?

I have taken real analysis, but never learned Fourier analysis. What is a good book to get started? I'm not sure the Stein book would be good.
26
votes
1answer
388 views

To what extent were mathematicians in previous centuries aware of the lack of rigour in their methods?

By modern standards, much of pre-modern mathematics isn't rigorous. Famous examples include Euler's solution to the Basel problem or literally anything involving sets before Cantor and Russel came ...
2
votes
0answers
26 views

Proofs by analysing games

I recently read the following article giving a novel proof of the uncountability of $\mathbb{R}$ by analysing a particular game, amongst other results. ...
9
votes
3answers
270 views

What does it mean to be $0.9-$Dimension?

We can visualize $1\mathrm D$, $2\mathrm D$, $3\mathrm D$ and we can think of a higher $M-\mathrm {Dimension}$ where $M\in \mathbb N^+$as a vector. But I recently learned that there are non integer ...
4
votes
2answers
94 views

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...