Questions tagged [textbooks]

Questions about comparison of textbooks, the use of textbooks in mathematical education, requests about textbooks dealing with a specific topic in a specific way.

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43
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4answers
4k views

How to respond to “solve this equation” in a basic algebra class

I asked this question once on math.se, but don't follow the link unless you want to risk biasing your own response: https://math.stackexchange.com/questions/444696/how-to-respond-to-solve-this-...
33
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3answers
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A calculus book that uses differentials?

All introductory calculus books that I have seen spend most of their chapters on differential calculus talking about derivatives, with at most a short section defining differentials as $dy = f'(x) \, ...
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4answers
3k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
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Open-Source Math Textbooks

It seems to me that an open-source model could work quite well for textbooks, with issues being raised by the users of the book and different forks of the project being created for different ...
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6answers
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How do you go about writing your own lecture notes for a new course?

In advanced graduate courses, there are often no textbooks on the material being covered, and sometimes no good introductory material at all. Even when there are textbooks, many professors prefer to ...
25
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5answers
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"Opinionated" textbooks

It's been said that no one explains anything so well as when they are trying to persuade you of something. One of my favourite textbooks is E.T. Jayne's "Probability Theory: The Logic of Science". ...
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8answers
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What is a good reason to change calculus texts?

Our college is switching to an Early Transcendentals calculus text, and this seems like a good time to consider which text we are using in general. Larson, Stewart, Thomas, Briggs/Cochran, etc are all ...
20
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5answers
2k views

What does it take to find a good math book for self study?

I'm 20 and I never learned math properly in my highschool. I found my interest in math last year and I've been searching for books since then. I tried Khan academy but I have difficulty paying ...
20
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2answers
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Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found

Over the years I have occasionally encountered a number of Algebra 2 textbooks that make an incorrect (or at very least extremely misleading) claim along the lines that "all solutions of a polynomial ...
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359 views

Is required reading of the text effective, and how can it be assessed?

This will likely depend on the class, of course. But I've asked calculus students in the past if (a) they regularly read the textbook and (b) whether this is helpful for them and (c) whether they like ...
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4answers
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How can I choose a free calculus textbook?

As I have been recently informed, it is a good idea to consider free calculus textbooks for college and university courses. However, this feels risky to me, because: I don't know anyone who is using ...
18
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4answers
577 views

What are the major obstacles to crowdsourcing a competitive, free calculus text?

It is well known that Allen Hatcher has created a free textbook for algebraic topology that is high enough quality to be used in a large number of graduate courses in the united states, saving ...
17
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4answers
660 views

What reasons are there preventing me from using an old edition text?

Background: I'm a final-year math student applying for faculty jobs at small schools in the US. I'm currently designing a few courses, and this questions has been bothering me for some time now: Why ...
17
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1answer
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Linear algebra textbooks presenting an eclectic, geometric approach to the subject

I am teaching an undergraduate course in linear algebra this fall. I am dissatisfied with most existing textbooks, and indeed with the way in which this subject is usually taught. I hope to find a ...
16
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5answers
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Best textbooks to introduce measure theory and Lebesgue integration?

What are the best textbooks to introduce measure theory and Lebesgue integration to undergraduate math majors? Many students in such a class will go on to graduate school and be required to take a ...
16
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6answers
499 views

What are some of the qualities that accessible textbooks share?

Many, perhaps most, math textbooks are very hard for most people to dive into. A few textbooks are delightful, and encourage people to learn math by their engaging tone. What textbooks have helped ...
16
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1answer
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Is MacLane and Birkoff's "Algebra" suitable today as either an undergraduate or graduate text in abstract algebra?

I'm going to soon review the 3rd edition of Saunders MacLane And Garrett Birkoff's Algebra at my blog soon and this is the first time I'm really carefully reading it. While I'm really enjoying the ...
16
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1answer
503 views

Textbook for multivariable calculus with interesting modern applications

A colleague of mine in a math department at another university is looking for a textbook on multivariable calculus that discusses applications of higher-dimensional integrals that feel contemporary ...
15
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6answers
986 views

Where can I find resources for creating a mathematics “bridge course”?

I originally asked this over at MathOverflow, but it was suggested I might also find some good answers over here. My university department is in the very early stages of developing a "bridge course" ...
15
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7answers
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What are the differences between popular undergraduate abstract algebra books?

I will be teaching a year-long undergraduate introduction to abstract algebra in the fall, and I am quite looking forward to it! I need to choose a textbook, and I don't have personal experience with ...
15
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5answers
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Cost and benefits of compartmentalization in k-12 curriculum

This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic. K-12 mathematics textbooks (understandably) divide ...
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7answers
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Why don’t American school textbooks recognize negative numbers as whole numbers?

Looking up for definition for whole numbers on Google yields a result which mentions: The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). I ...
14
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4answers
437 views

When Euclid was used as a textbook, what exercises did students do?

Until fairly recently, it was common for students in school to learn Euclidean geometry from a translation of Euclid. I get the impression that ca. 1700 this would have been in college and only for a ...
14
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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 ...
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4answers
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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 ...
14
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3answers
276 views

Resources for teaching Riemann integration in higher dimensions and on submanifolds, with view toward Stokes' theorem?

Question I am looking for suggestions of good resources (textbooks or lecture notes preferably) for teaching Riemann integration in $\mathbb{R}^d$ with $d\geq 2$ and also for Riemann integration ...
14
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2answers
555 views

First year undergraduate text that teaches calculus using probability as a primary motivating example?

There has long been debate about whether a first year undergraduate course in discrete mathematics would be better for students than the traditional calculus sequence. The purpose of this question is ...
13
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3answers
288 views

Using Several Textbooks in a Course

Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in ...
13
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2answers
746 views

Why are hand waving arguments made in textbooks of undergraduate analysis and how should readers deal with them?

Having read several undergraduate textbooks in complex analysis (Stein-Shakarchi, Gameline, etc.), I find that some "hand-waving" arguments are frequently used. An example (the proof of the ...
13
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3answers
522 views

Without a constraint of time, is self-study with math textbooks better than college courses?

This question is about mathematics only. My forethought is that courses are usually based on textbooks, but they have less content than the textbooks. There are less problem sets, and chapters are ...
13
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3answers
305 views

Open Education Resources

We will be hosting an Open Education Resources workshop at the college where I work. I am one of the two faculty that uses OERs and was asked to speak about the pros and cons of using OER. What ...
13
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3answers
484 views

Teaching Infinitesmals and Non-Standard Analysis

This question is asked from a self-teacher standpoint(I am currently trying to learn more about non-standard analysis on my own), but I'd think it could be applicable to educators also. What are good ...
13
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3answers
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Is it a bad idea to use an old textbook such as Differential and integral calculus, with examples and applications for calculus course?

I am wondering if it is a bad idea to use an old textbook, such as Differential and integral calculus, with examples and applications by George A. Osborne. This book was published in 1906 and there ...
13
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1answer
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High-school level algebra textbooks for gifted students

Note. I asked the question below on Math Stack Exchange (link), but didn't get a really satisfactory answer there, so I'm posting it here too. I am looking for high school algebra/mathematics ...
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3answers
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Conceptual Mathematics by Lawvere & Schanuel as text for bridging course?

I have recently come across Conceptual Mathematics: A First Introduction to Categories by Lawvere & Schanuel. It is a gentle introduction to Category Theory and strikes me as a potential ...
12
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5answers
780 views

An application-heavy functional analysis textbook?

I took functional analysis from Conway's book. I thought it was just as abstract and dry as homological algebra, if not more. I knew of no applications. Then I learned that standing waves on a drum ...
12
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4answers
870 views

The Order in Pre-Calculus Textbooks

Every Pre-Calculus I have examined starts with functions in general, then polynomial and rational functions, followed by exponential and logarithmic functions and Trigonometry, and ending with ...
12
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2answers
422 views

How to divide up readings in a flipped classroom?

Next semester I plan to experiment with "flipping" a classroom, by assigning required readings from the textbook (perhaps with supplementary notes) so that lecture doesn't have to "cover all the ...
12
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3answers
570 views

Is it a dead end to define differentials as finite differences on the tangent line?

In a freshman calculus text (Larson), I was surprised to find a definition of differentials as finite differences on the tangent line, and even more surprised to learn later that this definition ...
12
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5answers
632 views

Geometry with a view towards differential geometry textbook

I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or ...
12
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2answers
207 views

Do "overview" sections increase learning outcome?

I write a math textbook for which I want to make an overview chapter for each part of the textbook. In those overview chapters I want to motivate and introduce the new mathematical concepts. I also ...
12
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1answer
386 views

Introduction-to-proof book using natural-deduction-style rules?

Can anyone recommend a textbook for an introduction-to-proofs bridge course that discusses the rules for "proving and using" (aka "introduction and elimination") each connective and quantifier, as in ...
12
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1answer
303 views

Probability textbooks repository

(This question was posted more than two years ago on math.stackexchange.com and, although there were some worthwhile answers, none actually answered the question as phrased.) Has anyone compiled a ...
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5answers
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Book request: teaching proving and reasoning at an American university

I am a European postdoc who recently teaching at a large public university in the United States. I will have to teach a course for undergraduate students that introduces them to proving and reasoning ...
11
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5answers
335 views

Pedagogical considerations behind current order of presentation of trigonometry

A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order: 1- Angles 2- Trigonometric functions defined on the unit circle 3- Right triangle ...
11
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1answer
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Is Lax's Linear Algebra and its Applications comprehensive or idiosyncratic?

I'm looking for a good abstract linear algebra text (i.e., not matrix crunching) for students who have completed a Strang-level linear algebra course plus exposure to a proof writing (e.g., induction ...
11
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2answers
179 views

Transitioning from 'Read textbook to learn' to 'Read original paper/Read paragraphs of textbooks'

I wanted to ask the following on Mathematics stack exchange, but checking the help centre, it appears that this site is more relevant: "Mathematical education, especially about teaching and pedagogy: ...
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2answers
192 views

2D drawings of 3D objects in printed school textbooks: orthogonal or perspective?

There is a tradition in the use of orthogonal projections to represent 3D objects in printed school math textbooks. On the other hand, perspective projections represent better the way as we "see" real ...
11
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0answers
352 views

Shanghai math -- what is it, and how good is it?

Some schools in the UK are adopting English translations of a grade school math textbook from Shanghai. The book appears to be designed to work with a specific teaching approach, the only specifics ...
10
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2answers
3k views

Why are all educational textbooks copyrighted? ©

I had an idea to improve education in my country with the help of textbooks by popular authors. I thought to publish videos on YouTube with comments and practical explanations about what the author ...