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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1answer
48 views

Reference Request: Suitability of a text and corresponding video lecture series request for "Matroid Theory"

I am an undergraduate student from the CS background. While reading a portion of the text "Introduction to Algorithms" by Cormen et. al. I came across a section of Matroids. I was unable to ...
3
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1answer
237 views

English translation of Sung-Dae Hong's The Art of Mathematics

The Art of Mathematics by Sung-Dae Hong is the standard high-school mathematics textbook in South Korea. The series gets new editions and reprints since 1966. Wikipedia has a page for it. Had it ever ...
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4answers
356 views

Textbook to study group theory as a part of Discrete Mathematics

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...
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1answer
133 views

Advanced textbook for vector fields [closed]

I am currently reading Spivak Calculus on Manifolds and Munkres Analysis on Manifolds. I am looking for a more advanced text, especially on vector fields as they relate to the great conserved fields ...
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5answers
361 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
259 views

Reading old or ancient texts in mathematics

I am recently wondering whether it is a good idea to read old (or very old) books in mathematics. In high school level, some people suggest students who are interested in geometry to read Euclid's ...
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4answers
439 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 ...
3
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1answer
858 views

Which book should I refer to for analytical solid geometry?

I am an undergraduate student and since this is a site of math educators, I thought of putting this question (more accurately a query) here. Can you list some good books on analytical solid geometry?
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5answers
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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 ...
3
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1answer
121 views

Dolciani and Sorgenfrey textbook collaboration

Would it be possible to get a complete list of math textbooks written jointly by Dr. Mary Dolciani and Dr. Robert Sorgenfrey? I'm particularly interested in focusing on how they collaborated while ...
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2answers
159 views

Is evaluating a Real Polynomial at a Complex Value a suitable task for Precalculus students?

In Korea, basically every teaching material for 10th grade math(about the level of precalculus) contains this kind of exercises in their first treatment of complex numbers: Evaluate $f(x)=4x^4-8x^3+...
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269 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 ...
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2answers
193 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 ...
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8answers
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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 ...
8
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3answers
240 views

Evaluating textbooks in math and physics

I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this ...
6
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1answer
100 views

Data on textbook adoptions in universities (math/science)

Does anybody know if there is a website/database/... on textbooks adoption in the US or some other country? (math/science textbooks) It would be interesting to see which textbooks are (and have been) ...
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2answers
256 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 ...
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3answers
2k 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 ...
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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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6answers
296 views

What do I study in calculus beyond the minimum required for undergraduate engineering?

I am majoring in aerospace engineering. I love math a lot, especially calculus. I have a lot of free time right now and I want to learn more stuff in calculus that would be helpful for my major but I ...
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2answers
342 views

How to teach linear programming and reductions?

Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs,...
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5answers
340 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 ...
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2answers
196 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 ...
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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 ...
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4answers
318 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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1answer
116 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 ...
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2answers
1k 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
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1answer
132 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 ...
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5answers
840 views

Writing a Calculus textbook for a course I am creating

Using LaTeX, I am attempting to write a single-variable calculus textbook that gives the reader an understanding of calculus and its applications without a lot of the fluff I have seen in many other ...
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3answers
531 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 ...
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6answers
994 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" ...
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3answers
1k 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. ...
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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 ...
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3answers
299 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 ...
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2answers
198 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
169 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 ...
5
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3answers
252 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 ...
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2answers
162 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 ...
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 ...
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1answer
127 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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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 ...
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0answers
120 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 ...
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1answer
353 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 ...
13
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2answers
770 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 ...
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0answers
224 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 ...
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2answers
546 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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3answers
2k 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 ...
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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 ...
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1answer
179 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 ...
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0answers
115 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 ...