Questions tagged [reference-request]

A reference request is a request to be provided with (links to) documentation, official papers, and specs related to one or more specific algorithms or mathematical procedures, to provide a trusted base for what's being said or written.

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11
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6answers
1k views

Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"

Advanced engineering mathematics is a subject of its own, building up from simple notions of functions, series, integration techniques and brief review of linear algebra which leads to transform ...
8
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2answers
366 views

Symmetric version of product and quotient differentiation rules

The usual way of writing the product rule and the quotient rule in differentiation is $$(fg)'=f'g+fg'$$ $$\left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^2}\quad\text{where}\quad g\ne 0$$ A few years ago, ...
18
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3answers
418 views

Critiquing Proof Style During Class

I would like to spend a day with my students analyzing mathematical writing. One way I might accomplish this is to offer multiple proofs (some good, some poor) of the same simple statement and ask ...
8
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1answer
318 views

Quantity as the basic concept for applied mathematics

I read about the Theory of Quantity in the booklet Principles of Mathematics Education written by Kô Ginbayashi in 1984. (A summary of it is here.) Instead of using pure numbers as the basic concept,...
14
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4answers
6k views

What is a good book to learn all of prealgebra?

I am an old man trying to learn math, starting off with prealgebra and need a good comprehensive book for it. The book should NOT contain annoying images like in most American textbooks or anything ...
4
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2answers
632 views

List of math competition problems by topic

I am working with a student who is very interested in math competitions, and I am teaching him Algebra I. I feel like doing competition problems related to a given topic is an excellent way to force ...
8
votes
1answer
59 views

Sources for embedding secondary math into technical classes?

I've taken a job for the next school year, which will involve embedding secondary math (algebra, geometry and trigonometry) into technical programs such as drafting and electrician school. Does ...
6
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1answer
124 views

Reference request: Textbooks in mathematics for future kindergarten teachers

The title says it all, but some more details. We need good textbooks for a mathematics course for future kindergarten teachers. The actual course is titled (my translation) "Text, language and ...
13
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3answers
359 views

Resources for reading mathematics out loud in different languages

Are there reference books or online material for reading mathematics out loud in different languages? For example, the expression1) $$ \int x^2dx=\frac13x^3 $$ is understandable to anyone who has ...
15
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4answers
2k views

Teaching a very enthusiastic and bright 5 year old

I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never tought at this age and I am unfamiliar with the ...
22
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3answers
385 views

Mathematic reasoning in nonEnglish/non Western languages

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language ...
8
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3answers
338 views

Have there been longitudinal studies comparing outcomes of various teaching methods?

There have been many innovative teaching methods tried from time to time. Twenty years ago was Calculus reform, now is flipped classrooms. We also have a resurgence of the Moore method under the name ...
15
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4answers
558 views

Thought experiment: Utopian college-level math curriculum without external constraints

An old favourite topic of mine to daydream about on pleasant afternoons is this: If you could completely redesign the university-level mathematics curriculum from the ground up to be as good as it ...
10
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1answer
224 views

Is there any footage of Let's Make a Deal illustrating the Monty Hall problem?

The Monty Hall problem is a classic probability riddle and I will be gleefully explaining it to my class of discrete math students. It is apparently based on his classic game show Let's Make a Deal. ...
39
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5answers
3k views

Effects of early study of advanced books

Context: There was recently a question on Math.SE: Inferior to Other Younger and Brighter Kids which starts as follows: I'm a high school student (Junior/Grade 11) and I'm currently studying ...
7
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3answers
193 views

References on British, German and French educational system

I'm writing a comparative study between mathematical teaching in my country (which sucks by the way) with others. However, I don't want to make it about today, globalization gives us a good notion of ...
10
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4answers
621 views

Creativity in mathematics

I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I ...
1
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1answer
85 views

In which order should I read these topics? [closed]

In which order should these topic be read if one have to understand mathematics topic well? Differential Equations Game Theory Graph Theory Linear Programming Probability Statistics Vector ...
8
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1answer
290 views

Why are manhole covers circular?

The answer to the question in the title, that then it will not easily fall down into the manhole (just try with ellipsoidal or square covers ...), is a property of circles I never learnt in school. ...
12
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1answer
227 views

Has someone written an essay on the role of axioms in mathematics (suitable for undergrads)?

I'm just starting up the academic year (yes, it starts in February here in the Southern Hemisphere) teaching a 2nd-year Introduction to Pure Mathematics class. For general background, I would like to ...
16
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1answer
338 views

How to assign grades to proofs: what do(es) the literature/experts suggest?

I am teaching an introductory course on proofs in mathematics in a mid-size American public university, and trying to develop some kind of consistent grading meta-scheme for grading proofs. I am ...
5
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3answers
1k views

Honors project idea for linear algebra

At my institution there is an Honors program which encourages (or requires) students to petition classes for Honors. Basically, what this amounts to is the student has to write a 10 page (not set in ...
3
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0answers
82 views

Student input in secondary teacher evaluations

this is something I have been wondering about for a while now. In my school district (urban setting in Pennsylvania) student input amounts to exactly 0% of the final assessment for observed teachers. ...
17
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7answers
578 views

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
7
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3answers
4k views

System of Equations Generator

I often find myself spending too much time coming up with systems of equations for exercises for my students to practice on (that come out to nice integers). For two variables this is trivial, albeit ...
21
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3answers
1k 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 ...
4
votes
1answer
159 views

What is a good reference for (this way of) generating a logarithmic scale?

I am interested in answers to the title question without parentheses, but I found this method below rather interesting, and I am hoping to find it published somewhere, along with a teacher's guide ...
12
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2answers
854 views

Resources on how to mark a maths exam

I am looking for some resources which tells someone how to mark a (1st year undergraduate level) maths exam paper. Ideally it would cover the basic stuff, like making an error at the top doesn't ...
8
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0answers
82 views

Literature on skill transfer

Motivated by this other question I'm interested in getting to know the literature on mathematics skills transfer within itself. All I know is what I've read in David Perkins's book "Knowledge as ...
14
votes
2answers
364 views

Research on how mathematics skills transfer to other areas

Briefly: I am looking for research on the extent to which learning mathematics (let's say "college algebra" if we want to be specific) impacts problem solving skills, abstract reasoning, etc. Less ...
12
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2answers
368 views

Mathematics and the hermeneutic circle

Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations. This leads me to ...
15
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3answers
458 views

Calculation versus writing in mathematics

Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
8
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0answers
280 views

What else we miss?

Context: Some time ago there was a post on a brief study conducted by Alexis Wiggins (she was shadowing two students for two days), you can find it here, which got quite an attention. One interesting ...
4
votes
2answers
275 views

Promoting intuition (for undergraduate students): visual thinking, geometic approaches, etc. in the classroom

Note: This question is ment to extend the scope of some related questions of mine. I would appreciate very much any suggestion to improve the way the question is posed. I would like to ask what is -- ...
13
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3answers
534 views

Immersive attention when learning mathematics

In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. ...
8
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5answers
414 views

Good resources for coaching for mathematics competitions (Highschool Level)

I'm teaching in China, and I have been told that I will be leading the students in mathematics competitions. I feel very ill prepared for this. I never did mathematics competitions in either high ...
2
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1answer
90 views

Mathematics necessary for signal processing

What is the mathematics needed to delve in signal processing? I don't know if it correct to dig toward purism downwards or stay at the applied level. Specifically, in complex analysis I find the $\...
1
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4answers
3k views

Prerequisites of mathematical analysis [closed]

What topics should I read before studying mathematical analysis? I want to have a solid foundation in terminology, notation and concepts in general. Please suggest titles for books.
12
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1answer
488 views

Teaching K-8 math in the style of "A Mathematician’s Lament"

Here's a link to the full paper, colloquially known as Lockhart's Lament: Link: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf In the context of K-8 learning materials that take ...
15
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2answers
815 views

The Fundamental Theorem of Calculus and Vegetables

When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who ...
12
votes
5answers
9k views

Real life examples to motivate the study of linear functions

Some years ago I used mobile phone or internet rates (for example, with basic fees and a given charge per minute or by data volume) to introduce and motivate the study of linear functions. However, ...
10
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1answer
189 views

Can we motivate undergraduates by saying they will be able to read famous papers?

I have a differential equations student who said the following (I'm paraphrasing of course): A long time ago, my math teacher told me that when I finished differential equations, I would be able to ...
7
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1answer
131 views

Resource about notation for students

Others have already here pointed out that students can struggle with notation in mathematics. I can often think that the lack of proper notation gets in the way of solving a problem correctly. ...
13
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0answers
265 views

Exercises to go with Simon's "Representations of finite and compact groups"

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had ...
11
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3answers
211 views

What to do when a math course needs too many shapes/figures and I'm not good at drawing?

Teaching some courses in mathematics requires drawing too many shapes or figures (e.g. Geometry, some parts of calculus, etc.) but I am not good at drawing shapes. Of course I can use slides, but I ...
9
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2answers
661 views

What caused the (relatively) recent popularity of set theory?

When I was growing up during the 1960s, "set builder notation" constituted a large part of what was then the "new math." Question: When and why did "set theory" become popular in math education? ...
8
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2answers
263 views

Teaching "and a half" early, possibly before general proper fractions

Fractions are a well-recognised issue in maths learning, with all sorts of complex issues involved. One particular aspect of this is difficulty recognising fractions as numbers which describe the size ...
8
votes
0answers
307 views

Guided Lecture Notes for Calculus

Last semester I taught Linear Algebra using the standard textbook of Lay. Online one can find nice "class handouts" that serve very well as lecture notes for students to follow along with during class....
10
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2answers
346 views

Term and reference for the problem of students “overassociating” concepts with each other

I am writing a paper directed at a physics-education journal and I want to briefly refer to the phenomenon of students “overassociating” (in lack of a better term) mathematical concepts with each ...
14
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3answers
1k views

Recommendations for inquiry based/aided discovery textbooks

I've recently dipped my toes into the world of number theory; and I've bought a book that to me is quite unconventional: R. P. Burn, A Pathway into Number Theory. I've yet to put the book through its ...