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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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157 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
votes
3answers
114 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 ...
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2answers
100 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 ...
0
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1answer
84 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
97 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
171 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
254 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
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1answer
138 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 ...
1
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3answers
186 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 ...
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3answers
192 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
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0answers
129 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
164 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
273 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 ...
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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
79 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
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1answer
126 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
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0answers
308 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
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0answers
106 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
121 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
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4answers
289 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
168 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
120 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
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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
114 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
129 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
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1answer
88 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
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3answers
343 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
95 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
228 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
140 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
360 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
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2answers
185 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
110 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
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2answers
454 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
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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
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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 ...
11
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3answers
272 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
81 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.
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4answers
196 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
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4answers
279 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
125 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
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1answer
1k 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 ...
10
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0answers
202 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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4answers
383 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
135 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
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4answers
572 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
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0answers
130 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 ...