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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.

9
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2answers
132 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 ...
1
vote
1answer
84 views

Geometry textbook with an abstract algebra emphasis

I'm teaching a variety of undergraduate and graduate geometry classes (mostly for in-service teachers) which range from elementary axiomatic geometry to more advanced transformational geometry. I'm ...
0
votes
1answer
97 views

Good textbooks for a college Basic Geometry course?

I will be teaching geometry for the first time ever this summer. I teach at a community college, and we only offer this course in the summer. (Mostly high school students take it, but it is a college ...
4
votes
3answers
135 views

Calculus workbook suggestions

Context: I am an assistant professor of mathematics at a small institution in the US. Our department uses Stewart's Essential Calculus for our calculus sequence, but I find that my students and I are ...
2
votes
0answers
121 views

According to Nathan Jacobson, what is Intermediate Algebra and Advanced Algebra?

Nathan Jacobson's Basic Algebra I, II covers many topics in Algebra that is probably even beyond many pure mathematics full professor's scope of knowledge, unless the professor is specialised in ...
6
votes
2answers
157 views

Vector calculus texts that are free-as-in-speech?

I'm looking around for a text that covers vector calculus and multivariable calculus, and that is also "free as in speech," not just "free as in beer." In other words, I'm looking for texts that are ...
12
votes
3answers
1k views

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 ...
7
votes
2answers
260 views

Structure of math textbooks

Math textbooks for undergraduate and graduate students are almost always structured in the same way. Each chapter/section/etc. has it's definitions, theorems, propositions, etc. with proofs following ...
18
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2answers
2k views

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 ...
1
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0answers
77 views

What are mathematical definitions? How are they decided upon? [closed]

What are mathematical definitions? When(at what stage) and how do mathematicians come up with the basic definitions of the new mathematical concepts they have found? I BELIEVE in math I BELIEVE it's ...
4
votes
1answer
120 views

Open Rings-First Abstract Algebra Text

Building off my own experience and the responses to "Rings before groups in abstract algebra?" I've decided to teach Abstract Algebra using a rings-first approach. However the various texts mentioned ...
1
vote
0answers
214 views

Writing Up Solutions To G.H. Hardy's A COURSE IN PURE MATHEMATICS?

Ok, this may be a ridiculous question and if so, you guys will shut it down. But I didn't know where else to ask it-it certainly doesn't belong on Math Overflow. Does anyone know if anyone ever ...
3
votes
0answers
104 views

On concentration inequalities [closed]

I would like suggestions for a good text on concentration inequalities (examples here https://en.wikipedia.org/wiki/Concentration_inequality). I am looking for sources (texts) that can give strong ...
1
vote
0answers
106 views

I’m considering buying Art of Problem Solving. For those who read it, what’s your review of it? [closed]

As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...
8
votes
4answers
278 views

Should I go over examples straight from the textbook in Calculus lectures?

Let's say I'm teaching an undergraduate Calculus 1 course using Stewart's Calculus textbook. Should I spend a fair amount of time in lecture doing examples that are taken straight from the textbook ...
3
votes
4answers
166 views

What are standard (or good) textbooks for undergraduate graph theory?

I'll be teaching graph theory this fall for the first time. The only undergraduate graph theory book I am familiar with is Doug West's book, which I like. But I'd like to consult some other ...
3
votes
2answers
114 views

Supplemental text for undergraduate real analysis

Context: I am an assistant professor at a small college in the US. Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the ...
7
votes
3answers
1k views

Why don't textbooks foreground marginally generalized theorems?

'Marginally generalized theorems' refers to theorems that were generalized so marginally that they can still be taught, and understood by the students, in the same course. Examples of theorems NOT ...
9
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0answers
111 views

Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry ...
3
votes
3answers
121 views

English book for math for (electrical) engineering similar to German “Higher Mathematics”

Many universities in Germany have special math courses for engineers. These courses are often called "Höhere Mathematik" (higher mathematics) or "Ingenieursmathematik" (engineering mathematics). The ...
4
votes
1answer
85 views

Is there a way to report errors in K-12 textbooks?

I imagine it varies by publisher, but I was just working with a student who uses the textbook Big Ideas Math Accelerated: A Common Core Curriculum by Larson and Boswell, and I found an error within ...
7
votes
3answers
329 views

Teaching Calculus Less Formally

I'm wondering if anyone knows of calculus books or other work towards teaching calculus in a less mathematically rigorous way. I'm thinking mostly of American-style college level calculus courses ...
2
votes
0answers
92 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
4
votes
3answers
217 views

Could you recommend a book for studying calculus 1?

I would like to practice a large quantity of exercises from limit calculation, derivatives, sequences and series and finaly integrals.
2
votes
1answer
105 views

books to teach K-12 math/science via real-world approach?

I volunteered abroad in rural Ethiopia and a village in a remote mountainous area of China. I plan to return to both places and teach for as long as I can make it work. I want to focus on STEM, but ...
-1
votes
1answer
136 views

What textbook is this chapter from? [closed]

I was looking for a good explanation text on single-variable calculus, especially limits, introduction and examples. I found this pdf and I really like it and would like to read the whole book. I was ...
10
votes
1answer
298 views

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 ...
8
votes
1answer
2k views

Odd or Even-Numbered Answers in Textbooks

Why do some math (and science) textbooks/solution books only include answers to odd- or even-numbered problems? Some textbooks have a separately purchased answer book with the missing answers, while ...
7
votes
2answers
162 views

“Personalized System of Instruction” (PSI) vs. “Individually Prescribed Instruction” (IPI)

This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the ...
3
votes
1answer
109 views

Dissemination of mistakes in international texts such as the IGCSE

I started tutoring IGCSE Mathematics. In preparation for just a 1 hour class for 1 student, I noticed at least 3 mistakes (confirmed with their replies to me) in Chapter 21 of the Haese 0607 book (...
13
votes
1answer
322 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 Cauchy ...
4
votes
3answers
118 views

Sites/books with math problems for bright 5th graders

I'm looking for sites, or books, for bright 5th graders or above, with math problems and respective solutions.
10
votes
5answers
1k views

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
votes
3answers
267 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 ...
0
votes
1answer
78 views

Text book on real analysis for undergrad in statistics

May I get some recommendation on text book on real analysis for undergrad in statistics? Thank you.
2
votes
4answers
191 views

The sequence of chapters

I'm using a textbook but in my course the chapters are numbered differently. For example, the book has the following chapters: Real Numbers Square Roots Polynomial in a single variable (they don't ...
6
votes
4answers
277 views

What science books would you recommend a curious middle school student to read at home?

OK, this is not exactly a Math Education question, but in lieu of a functioning Science Education site and because in middle schools Math and Science are often taught by the same teachers, I'll ask ...
6
votes
2answers
119 views

Recommendation for an introductory operations research book

In the spring I'll be teaching introductory operations research at an undergraduate liberal arts college in the US. The target audience consists of applied math majors and students in our ...
10
votes
1answer
814 views

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 ...
9
votes
0answers
190 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
votes
4answers
375 views

Surrounding a subject and strangling it to death versus concentrating on the main point

Standard calculus textbooks begin by introducing limits, including limits of a fraction as the numerator and denominator approach $0,$ limits of a fraction as the numerator and denominator approach $\...
8
votes
2answers
133 views

Textbook search: learning the math required to read the newspaper

TL;DR: do you know of an undergrad textbook that covers numeracy with an emphasis on genuine context (as opposed to the artificial word problems that are all too common)? Less concisely: I am an ...
11
votes
4answers
557 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 ...
6
votes
0answers
126 views

Which calculus textbook is aligned the most with the CollegeBoard course description?

The CollegeBoard website lists many AP calculus BC references. But it also mentions that "The materials on this List range in alignment from 59% to 100%." So, which of them is aligned the most with ...
42
votes
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-...
6
votes
2answers
284 views

Looking for a “Stable” College Algebra Textbook

I have taught College Algebra several times and will teach it again in the next semester. College Algebra, according to the the catalogue of my college, is described as follows: This course ...
2
votes
1answer
83 views

Preparatory text/s for Boas' Mathematical Methods in the Physical Sciences? [closed]

Assuming that I remember only basic arithmetic, what (if any) mathematics must I learn before tackling Boas' Mathematical Methods in the Physical Sciences?
11
votes
2answers
161 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: ...
3
votes
1answer
264 views

Good Textbook for combined Beginning and Intermediate Algebra Course

We'd like to create a course that covers beginning and intermediate algebra in one course (8 hours a week), getting students ready to succeed in precalc and calculus. I am at a community college. I ...
5
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2answers
118 views

Great Worked-out examples books for Mathematics

I'm studying Mathematics in the UK. Back in Italy, where I am from worked-out problems books are very popular in mathematics and they are always recommended or compulsory at university. Going through ...