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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25
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5answers
1k views

"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". ...
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 ...
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 ...
8
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1answer
477 views

"Probable" vs. "Likely"; Choosing the Appropriate Word

In some school textbooks, before introducing the probability as a number between $0$ and $1$, the words "likely", "More likely", "less likely" etc. are used to indicate the likelihood of an event. ...
10
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3answers
314 views

Discrete Math text before a proof course

Our department has decided to offer a "Discrete Math" course that students would take before their "Intro to Proofs" course. The idea is that the Discrete Math course would focus on the computations ...
7
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5answers
2k views

Best rote high school algebra textbook?

I am looking in too getting a textbook for my son who I will be teaching algebra soon (homeschool). I don't like math, never did and am not very good at it. Quite frankly, my son isn't good at it ...
8
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2answers
336 views

A companion on the Journey Through Genius

I find William Dunham's book Journey Through Genius is a great text to use in a History of Mathematics course, but I wish it had more textbook-like content, e.g. reading comprehension questions, ...
4
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2answers
523 views

Open source lecture notes textbook in "introductory real analysis"

So far I wasn't able to find one single open source set of lecture notes or textbook with $\LaTeX$ source code available on "introductory real analysis" that could suit my needs. It seems to me that ...
8
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3answers
292 views

Lie Theory: significance and relevance to undergraduate education

I have been strongly recommended to read the book Naive Lie Theory. In the introduction one can read: "This naive approach to Lie theory is originally due to von Neumann, and it is now possible to ...
9
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2answers
283 views

Differences between Hardy&Wright and Ireland&Rosen for number theory course

My professor advised us to get either Hardy&Wright or Ireland&Rosen for our introductory number theory course. I would like to ask what are the differences between these textbooks in terms of ...
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 ...
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 ...
6
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3answers
4k views

Lang's Linear algebra or Introduction to linear algebra for an undergraduate

From a pedagogical as well as strictly mathematical perspective, which one of Lang's Linear algebra and Introduction to linear algebra would you recommend to an undergraduate with not much experience ...
7
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1answer
410 views

Is there a repository with K-12 math exercises and problems written in LaTeX (English or Spanish)?

I've been searching for a repository or a database with math problems (K-12 levels) written in LaTeX, but with no luck. Neither in Spanish (my student's language) ...
4
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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 -- ...
10
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3answers
2k views

Pedagogy, mathematics and Dieudonné's Foundations of Modern Analysis

I've heard from a friend of mine that Dieudonné's Foundations of Modern Analysis is "painful reading" and "a little outdated"; however, my teacher actually suggested it to me, describing it as a "...
4
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1answer
207 views

Honors Level High School Coursework Curriculum?

My wife and I will be homeschooling our son and twin daughters. We're interested in adopting an honors-level mathematics curriculum for secondary students that culminated in calculus AB in 12th grade. ...
19
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4answers
1k views

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 ...
21
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8answers
3k views

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 ...
6
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2answers
460 views

Differential equations book

I am looking for a book on differential equations (ordinary/partial) of a particular kind. I figure out I am terrible at solving differential equations. This a vast field and unfortunately I don't ...
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 ...
10
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2answers
502 views

Textbook for 2nd linear algebra course

I am teaching (for the first time) a 2nd course in linear algebra. The students will have had a beginning course in linear algebra and a beginning course in abstract algebra. I am considering Hoffman ...
15
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5answers
1k views

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 ...
6
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3answers
2k views

Arithmetic / Algebra problem generation software?

I'm struggling to find any good "problem generation" software or sites. I want a program that will do the following: Generate typical problems at all sorts of levels (from toddler age through to teen,...
6
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1answer
632 views

Why are textbook chapters so long?

I'm referring here to (math or other subjects) textbooks which include an exposition, main text and examples, references and exercises in each of the chapters. From my experience, in most cases, it ...
2
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0answers
125 views

Searching for an analysis textbook [closed]

Particularly, I'm looking for an undergraduate text with an excellent explanation of $\delta$-$\varepsilon$ proofs, and many example questions related thereto.
15
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7answers
3k views

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 ...
10
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2answers
793 views

Mathematical thinking skills for engineering students

A few months ago, I asked a question on teaching engineers mathematical thinking skills over at MSE. I also asked it a little later at The Mathematics Teaching Community, but traffic on that site is ...
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3answers
2k views

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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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 ...
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" ...
10
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3answers
573 views

References for "high-school mathematics from an advanced point of view"

What are some good references for high-school (or even middle-school) mathematics, written from an advanced point of view, especially texts written for prospective teachers? Some references were ...
3
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3answers
2k views

Why are most math textbooks so uninspiring; unless you already like Math? [closed]

Why are math textbooks so often boring? It requires some mental discipline to do math; cartoons can help make the principles easier to digest. The Mathematical Association of America has many FUN ...
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 ...
29
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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 ...
7
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3answers
692 views

Problem books at undergraduate level

I am an Undergraduate student ready to enter into Graduate School. I will be studying Mathematics. In my Undergraduate studies, I came across various Problem books and followed some of them. The ...
10
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8answers
5k views

Open Source High School Textbooks

Where can I go to find open source high school level textbooks? I'm especially interested in geometry and algebra, though probability and trig are also useful. I'm interested in rearranging and ...
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 ...
28
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4answers
4k views

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 ...
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 ...
25
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6answers
3k views

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 ...
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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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 ...
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 ...
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 ...
5
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2answers
412 views

Why does current mathematics education often ignore the analyses of complex number solutions on (systems) of non-polynomial equations? [closed]

I have discovered that current mathematics education often teaches students to emphasize all polynomial equations should have complex solutions. But starting from non-polynomial equations (e.g. $\sin ...
16
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5answers
7k views

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 ...
19
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5answers
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 ...
33
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3answers
2k views

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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