Questions related to the teaching and learning of mathematics.

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28
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2answers
800 views

English words in written mathematics

I recently marked over $100$ assignments for a multivariable calculus course. One question which a lot of people did poorly was proving a given set was open. Aside from issues relating to rigour and ...
6
votes
3answers
1k 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 ...
3
votes
3answers
2k views

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$ , and find the point on the curve closest to $P$.

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$, and find the point on the curve closest to $P$. What I did so far is : plot the y var from $x^2-y^2=1 ...
3
votes
1answer
97 views

Mathematical Journey text

Hi I am looking for a HARDCOVER book I read when I was younger. It is fairly modern and published probably around 2006 - 2007. It is a hardcover with a cheesey title like: Mathematical thinking ...
0
votes
2answers
2k views

How to find multiples of numbers under a certain range

I recently found a 'question' that requires me to find the sum of all multiples of 3 and 5 under 1000, I sadly cheated and found some code online to help build a code in python: ...
79
votes
22answers
9k views

The Best of Dover Books (a.k.a the best cheap mathematical texts)

Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books ...
1
vote
3answers
141 views

what are the rules/rationale for “simplifying” negative denominators

So I'm losing my mind trying to understand the rules and rationale behind "simplifying" expressions and equations in Algebra. It's been decades since I've had to study for it (going back and ...
4
votes
3answers
1k views

Does learning logic and set theory before arithmetic, algebra, and geometry have an advantage?

I'd like to become conversant in a wide variety of serious mathematics, but i'm currently one of those students who did very poorly on mathematical subjects in school, never completing even basic ...
3
votes
3answers
204 views

Learning Combinatorial Species.

I have been reading the book conceptual mathematics(first edition) and I'm also about halfway through Diestel's Graph theory (4th edition). I was wondering if I was able to start learning about ...
7
votes
2answers
539 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
7
votes
7answers
3k views

Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$

I'm looking for an understandable proof of this theorem, and also a complex one involving beautiful math techniques such as analytic number theory, or something else. I hope you can help me on that. ...
12
votes
2answers
2k views

Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
1
vote
2answers
366 views

The Game of Nim alternative solutions

Nim has a mathematical solution which uses binary number system and addition modulo 2.I was wondering if there is an alternative solution to this game or at least another interpretation of the ...
5
votes
2answers
831 views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
3
votes
1answer
109 views

Course/homework management systems for computational math courses [closed]

I will be teaching a course which will be based on a mathematical software, (as in MATLAB, MAPLE, Mathematica). The question is how to manage homework. Ordinary email is not efficient it seems. I am ...
2
votes
3answers
163 views

Darboux integral too sophisticated for Calculus 1 students?

I strongly prefer Darboux's method to the one commonly found in introductory level calculus texts such as Stewart, but I'm worried that it might be a bit overwhelming for my freshman level calculus ...
2
votes
0answers
115 views

What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...
2
votes
1answer
68 views

Why are variables typically given names like x in math?

Why do equations typically have variable names like x and y? In computer programming, we value meaningful names for variables. For example, if I were trying to calculate a square root, I would call ...
10
votes
5answers
331 views

High-School Level Introduction to Dynamical Systems

In one month I'll be giving a talk to motivated high schools students on a topic of my choice from dynamical systems and/or ergodic theory. I'm having trouble coming up with a topic compelling enough ...
2
votes
2answers
153 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 ...
0
votes
2answers
54 views

Profit loss or quantitative aptitude problem

At what percent above the cost price must an articles be marked so ás to gain $17$% after allowing a discount of $10$% ?
15
votes
2answers
639 views

How to deal with exercises with no solutions given?

Probably most people will acknowledge the importance of doing exercises when reading a mathematical textbook. Here I am talking about a textbook of similar level as those ones listed in GTM. However, ...
2
votes
3answers
133 views

teaching concept of “subspace” to linear algebra students

I'm currently a T.A. for an introductory combined linear algebra & differential equations course geared toward engineering students. One major problem I've run across is that most of my students, ...
8
votes
1answer
139 views

Proof vs Practice

I've been brushing up on a lot of basic arithmetic, algebra, and logic as I work towards a review of calculus (and beyond), and I keep noticing that in order to fully understand many principles in the ...
0
votes
1answer
319 views

Name of odd powered polynomial graph (Opposite of parabola(ic))

I am writing an assignment and have to describe the graphs for when the powers are even and when they are odd. I described the even power graphs as being parabolic or parabolas. The only problem is, I ...
0
votes
1answer
95 views

How would I take multiple single bit binary numbers and convert it into a single binary array number?

So lets say I have these: 101010101001 Now lets also say I didn't count them you should count binary, lets say I counted that number at 6 because their are 6 1s and the 0s don't count. Now how would ...
9
votes
1answer
266 views

General question: What one can do to help students one is grading?

Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science ...
0
votes
1answer
790 views

Learning a foreign language for math PhD

Many graduate programs in math require students to pass a foreign language exam in French, German, or Russian. Why is this so? Haven't the important mathematical works in these languages been ...
0
votes
1answer
16 views

Representing expression through a Summatory

I need represent this expression $L_{u_3}u(k-1)+L_{u_2}u(k-2)+L_{u_1}u(k-3)$ by using a summatory, $L_{u}$ is a vector that contains d elements $L_u=\begin{pmatrix}L_{u_1} L_{u_2} ...
10
votes
4answers
2k views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
16
votes
4answers
470 views

Mathematical Habit

Whenever I have to do proofs or understand a concept, I start with examples and generalize. As an aspiring mathematician, I have fears that it might hurt me, especially when we have so many ...
525
votes
151answers
33k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
2
votes
2answers
912 views

What are the drawbacks of multiple-choice questions? [closed]

I can easily understand the advantage of multiple-choice questions for instance in grading and so. A drawback is that real life problem don't have multiple choice questions all the time for instance ...
3
votes
2answers
172 views

Which set of subjects has the most algebraic 'flavour' to it?

I'm finishing my undergraduate mathematics programme this summer. The graduate program at my university requires that you specify a specialization on entry. This is very difficult for me and would ...
0
votes
1answer
94 views

Doing research on Google Matrix and PageRank algorithm

I'm doing research on Google Matrix and PageRank algorithm. In a paper, there are terms that I'm unaware of, such as stationary distribution, stochastic matrix, convex combination, markov matrix, ...
1
vote
0answers
139 views

Textbooks for PDE after Folland

I am a student who has just finished Folland's nice book Introduction to Partial Differential Equations. And I also read L. Craig Evan's textbook before. Could any expert here suggest a PDE book in ...
2
votes
2answers
107 views

Mathematically-based online games

I am looking for online games or puzzles which have a mathematical flavor and are suitable for general audiences. A classical example is the online version of Set Card Game. Or this game that has some ...
2
votes
0answers
78 views

Proving two Dedekind cuts represent the same number.

Hey guys I have a quiz soon and I really dont know how to prove this question. I tried my best but it is not working. Please help out with anything or hints. Let $(A'_1, A'_2)$ be a Dedekind cut of ...
-2
votes
2answers
280 views

Why mathematics has to be too much formal? [closed]

This is very general question I am asking here. But I think it really needs to be addressed. Whenever I come across a new concept in mathematics, I try to understand it by searching on the internet. ...
5
votes
3answers
140 views

Is there a simple geometrical description of $e$? [duplicate]

Of course I am not looking for a definition through $\int_1^e{1\over x} \, \mathrm{d}x=1$ or that slope of $a^x$ at $x=0$ is $1$ when $a=e$. I am looking for something understandable by a kid who has ...
1
vote
2answers
967 views

convert decimal 1024 to hexadecimal

I need to convert the decimal number 1024 to an hexadecimal number, I do this using these steps http://www.wikihow.com/Convert-from-Decimal-to-Hexadecimal#steps However, whenever I divide 1024 by 16 ...
0
votes
3answers
760 views

What is the most suitable function for a heart? [duplicate]

I have seen some codes to plot heart on matlab, e.g. first example second example How can I prove/find from the theory how to plot a perfect heart?
7
votes
5answers
328 views

Simplest error detecting/correcting codes for math newbies

Suppose you have been given the task of teaching some basic coding theory to folks who are interested in math but have not taken algebra, number theory, etc. If you want to introduce codes, you might ...
1
vote
1answer
105 views

What material is good for Atiyah-Singer index theorem [duplicate]

I want to ask what materials or books can I use to learn the proof of Atiyah-Singer index theorem? I hope such material contains enough preliminaries and background instead of proving the theorem ...
4
votes
1answer
191 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 ...
3
votes
1answer
677 views

Math refresher that covers several courses?

This is my first post in Mathematics but I'm not new to these forums. I use stakoverflow as I'm in software as a professional. This is going to be long post - not to mention a lot of what may seem a ...
2
votes
6answers
6k views

Which Mathematical Analysis I Book or Textbook Is The Best?

I'm in search of a mathematical analysis text that covers at least the same material as Walter Rudin's Principles of ... but does so in much more detail, without relegating the important results to ...
5
votes
1answer
282 views

What should I be doing in a grad level math course?

I have an undergrad degree in an engineering field and switched to applied math for a PhD. In engineering, I have had my share of good and bad professors but I knew what I had to be doing during a ...
1
vote
1answer
237 views

Determining Height of Tree

A surveyor needs to determine the height of a tree. She places a mirror on the ground and paces backwards until she sees the top of the tree reflected in the mirror. She marks where she is standing ...
1
vote
1answer
199 views

Question about the greatest lower bound of sets.

Let $A$ and $B$ be sets of real numbers. Define a set $A+B$ by $A+B =\{a+b|a \in A, b \in B\}$. Show that if $A$ and $B$ are bounded sets, then $g.l.b.(A+B) = (g.l.b. A)+(g.l.b.B)$. (The g.l.b. ...