Questions related to the teaching and learning of mathematics.

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15
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331 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
14
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0answers
2k views

What are some strong algebraic number theory PhD programs?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
11
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0answers
278 views

Anecdote about mathematicians leaping to tops of problems and then building a staircase down?

I've run across this cute little story before, and now for the life of me I can't find it anywhere. It goes something like: Two people are looking out onto a mathematical landscape, and there are ...
10
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325 views

How to be a bird

Freeman Dyson has famously characterized two styles of mathematics, that of the bird and that of the frog. I was asked recently the following question, which I don't know how to answer: If, in ...
8
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0answers
141 views

Undergrad research gateways

This question is intended as public service to mathematics. It is meant to benefit undergrad research students and maybe even researchers wishing to broaden their expertise and learn something away ...
7
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0answers
93 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
7
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0answers
875 views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
6
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0answers
58 views

Examples of useful, insightful and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
6
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0answers
159 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
107 views

Educational software for graduate mathematics

Our university uses computer software to help automate and expedite the learning process for basic math classes (college algebra, trigonometry, precalculus, etc.). Software such as this provides ...
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 ...
6
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0answers
365 views

Studying quantum mechanics without physics background

I am a first year PhD math student, and I am wondering if I should study quantum mechanics even though I don't have an undergrad background in physics. I posted this question in physics ...
5
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0answers
159 views

Comparing the U.S. undergraduate math education to the French “classes préparatoires”

Could anyone comment on how the math track of the "classes préparatoires" compares to the U.S. undergraduate major? I took a look at some of the French entrance exams and was rather intimidated. How ...
5
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0answers
136 views

Bayes analysis as used in a Presidential Election - with calculations shown

Can you show all the steps needed for a Bayesian probability progression as new information is received. As an example, initial estimate for Obama to win (popular vote) is 55%. In state-A, Democrats ...
5
votes
0answers
318 views

Derivation vs. proof

I imagine that Ramanujan and many other gifted mathematicians achieved results by derivation, meaning they followed a trail that led to a result, then proved it later if at all. Is this so and if so, ...
4
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0answers
63 views

From algebraic master degree to algebraic geomery Phd

I am a foreign master student in algebra at the final year. I'm familar with categorical algebra and have interesting in algebraic geomery and number theory. I have learned some knowledge about scheme ...
4
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0answers
55 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
4
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0answers
81 views

distance Pure Math graduate programs?

I would like to go to a graduate school for pure mathematics, but I do not live where such programs exits. Furthermore, I can not move. Question: Do any Universities have graduate program in pure ...
4
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0answers
542 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
4
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0answers
189 views

Mind Maps for teaching Mathematics

Has anyone used Mind Maps to teach advanced mathematical topics? If so, how did it work, was it useful or a waste of time? Thanks for any insights. Regards -A
4
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0answers
198 views

Starting my nephew out on the journey to higher mathematics.

My nephew is 8 years old and shows great promise as a student. Sadly, as most of you know most programs in secondary education don't offer any foundational courses for higher mathematics. What ...
4
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0answers
135 views

$\max_{y} \min_{x} f(x,y)$ as motif for exploring mathematics

It's been several years since my undergraduate math days, and I would like to spend a bit of time refreshing and then tackling a few things I never completely mastered. Rather than proceeding topic ...
4
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0answers
551 views

List of mathematical Summer schools (particulary in Europe)

I would like to apply for a summer school. Particulary it should take place in Europe and center on the topic numerical analysis. Is there something like a comprehensive list of summer schools?
4
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0answers
284 views

“Reverse thinking” exam questions-reference request

I am interested in exam questions that are "backwards" from how they are usually asked. For example: Brian and Megan have the following question on their exam: Find the volume of the solid ...
3
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0answers
97 views

Why is there no collection about all mathematical theorems and open questions?

I really would like to have a giant math collection which is sorted according to the Mathematics Subject Classification, but with more then 3 levels, and it should contain all known theorems and also ...
3
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0answers
52 views

Where to post a Calculus review guide?

I created a PDF document (using LaTeX) in which I wrote relevant review materials and Calculus problems for Calculus 1, 2, and 3. Is there an appropriate forum where I could try to post this to ...
3
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0answers
190 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
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0answers
73 views

Is there a link between level of abstraction and use of numbers?

One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an ...
3
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0answers
110 views

Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?

Let $x$ denote an arbitrary real number. Then $x^n$ makes sense for arbitrary $n \in \mathbb{N},$ via the obvious recursive definition. We can extend this definition by asserting that if $x$ is ...
3
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0answers
159 views

What is tensor, really?

How can one understands the definition of tensor from the purely formal point of view? To what abstract structure this concept can be generalized?
3
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0answers
125 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
3
votes
0answers
257 views

Graduate schools in set theory

What options for graduate schools are there for an aspiring set theorist? In the US, the only top 50 schools with active research in set theory seem to be Berkeley and Carnegie Mellon. Are there any ...
3
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0answers
126 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
3
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0answers
75 views

Niche topics in math useful for physics

I have a somewhat unorthodox question. What are some good niche topics that aren't typically covered in courses in math to self-study? Ideally, I'm looking for something that could ultimately be ...
3
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0answers
637 views

What should an undergraduate thesis be about?

I'm very excited to start my undergraduate thesis and I've heard some recommendations for topic but I have a questions and I'd like to hear your opinions. Should I look for the most advanced topic I ...
3
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0answers
204 views

How to Create a Lesson Plan with Wolfram Alpha

This will be my first post in this forum. I am so excited to see a lot of interesting posting from the community. From the FAQ, I learned that Mathematics stack exchange discussed about mathematical ...
2
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0answers
51 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
2
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0answers
23 views

Ratio Question (Primary School)

Now, there are 6 students who are sharing 4 desks at the library. While 4 of them are using the desks, the other 2 students have to wait and watch. If they have to use the desk for the same amount of ...
2
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0answers
60 views

First hand written draft Or LaTex typed draft; when some one want to publish?

When some one solve a math research problem and want to publish it somewhere; of course one should type it in LaTex. My Question: What should be the ideal way(time) to type it, I mean first one ...
2
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0answers
79 views

On which occasions will the intelligent layperson fail to recognize a mathematics problem?

Suppose an intelligent lay person is ignorant of mathematics and believes all the crap taught in classrooms to the effect that mathematics consists of believing dogmas, obeying instructions, and ...
2
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0answers
41 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
2
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0answers
140 views

What are some cool projects that can be done in a high school math class?

I'm studying to be a secondary math teacher and will be starting student teaching next month (an algebra 2 class). It's difficult to find activities and projects that are actually informative and time ...
2
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0answers
69 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
2
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0answers
99 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
2
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0answers
53 views

What is a sound curriculum for exponent rules in freshman algebra in high school?

We all know the the rules of exponents covered in freshman algebra. The question is, what is the best way to approach these topics as most 9th graders struggle in this area? I work as an after school ...
2
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0answers
66 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
2
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0answers
155 views

What is meant by “mathematical maturity”?

I have often heard people talk of "mathematical maturity", sometimes in the sense of the maturity required to understand an area of mathematics or in the approach to a problem or proof. However, it's ...
2
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0answers
48 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
2
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0answers
266 views

Math gre subject test scores and results?

I took the math gre scores back in October and did terribly (52%) even though I was scoring in the 70-80% on practice exams. I am interested in applying to Stanford's ICME and Berkeley's Stats ...
2
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0answers
118 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...