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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.

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2
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2answers
129 views

Which textbooks on College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE are written by world-class mathematicians?

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks ...
3
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1answer
119 views

Is there a rigrous and relatively complete book/lecture notes for selfstudying several variable calculus?

I would like to study university level mathematics on my own. I found rigorous books on single variable calculus and topology and learned those. But what would one recommend for several variable ...
6
votes
2answers
264 views

Is Plane Trigonometry by S. L. Loney still good as a textbook today?

I am considering using S. L. Loney's Plane Trigonometry as the textbook for my course in trigonometry and would like to ask for opinions about the book. This books is very odd and there might be pros ...
1
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1answer
106 views

Calculus book for basic calculus and repetition from videregående (Norwegian high school)

Does there exist a textbook in Norwegian (bokmål and nynorsk should both be fine) that covers the more advanced mathematics (needed for calculus) from videregående (secondary school, includes both ...
2
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2answers
143 views

High school maths textbook for talented students

I am looking for a math textbook. I'm 15 and I'd like to complete algebra 2 geometry and perhaps something about probability/ number theory or trigonometry would be nice too. Later I wanna do ...
2
votes
1answer
95 views

Is “The Petersen Graph” by Holton and Sheehan a good text for graph-theory students? Any requisite knowledge for mastering the text?

This book has been recommended to me by a guiding hand/mentor mathematician when I showed interest in his field, and he seemed to really like this book however he doesn't really know me and my ...
10
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5answers
218 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 ...
5
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2answers
116 views

Forming a Study Model for a Self-Study Beginner

I am very new to this platform so I may have misunderstood the intent of this site, or might seem a bit off, but please bear with me because I know what I want for certain. I always wanted to study ...
8
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3answers
328 views

MacLane-Birkhoff's “Algebra” vs Jacobson's “Basic Algebra I,II” vs Lang's “Algebra”

(Cross-posted at Math.Stackexchange) I'm searching for an apt textbook(s) on Abstract Algebra for a very advanced undergraduate/graduate level course in Algebra, and would be grateful for any help. ...
5
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2answers
185 views

What are the benefits of an expertly curated learning pathway?

What are the benefits of an expertly curated learning pathway? Like that provided by a major publisher's textbook - CPM, a school district's mandated curriculum - IM's Open Up Resources or a ...
4
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3answers
135 views

What books are good for drawing an intersecting plane?

I am looking for textbooks pertaining to drawing intersecting planes, intersecting point (among others) as follows. I am not sure this topic is taught in high school around the globe. That is why I ...
2
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2answers
110 views

Lower-division complex analysis textbook

I'm looking for recommendations for a good textbook to use for a hypothetical lower-division course in complex analysis, at a level of sophistication comparable to a second or third semester course in ...
1
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1answer
94 views

Roadmap to studying PDEs for analyzing Quantum Physics better

I am studying the basics of Quantum Physics (involving the characteristics of Schrodinger's Wave equation without actually analyzing it rigorously mathematically) this semester. I was wondering, ...
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0answers
110 views

Missouri EOC and the best Geometry book

I am a Missouri High School Geometry teacher. WE are adopting textbooks this year. I would like opinions on which books are most closely aligned with the Missouri Learning Standards because at the ...
0
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1answer
210 views

Gil Strang or Peter Lax? Which linear algebra book to use? [closed]

I have heard that Peter Lax's linear algebra book is the hardest you can find on the subject, but that it is the greatest linear algebra text in the world. But I also hear great things about Gil ...
11
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3answers
285 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 ...
4
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3answers
227 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
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4answers
251 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 ...
5
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3answers
212 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 ...
3
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0answers
157 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
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2answers
179 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
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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
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2answers
319 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 ...
19
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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 ...
4
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1answer
146 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 ...
3
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0answers
109 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 ...
8
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4answers
298 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
182 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
151 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
119 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
172 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
92 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 ...
6
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3answers
378 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
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0answers
100 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
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3answers
245 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
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1answer
110 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
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1answer
142 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 ...
11
votes
1answer
532 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
207 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
116 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 (...
15
votes
2answers
483 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
122 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
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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 ...
14
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4answers
330 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
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1answer
84 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.
1
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4answers
207 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
294 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
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2answers
135 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 ...