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.
168
questions
3
votes
1answer
112 views
Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?
I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
3
votes
1answer
140 views
How much literature research should one do when designing a course?
For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, ...
1
vote
2answers
90 views
Are books as old as J.E. Thompson's “for the practical man” series outdated?
I'm sure Thompson's books were a fine series back in his time, but are they still worth recommending for, say, interested high-school students or prospective college students that want to brush up ...
1
vote
0answers
62 views
Would the SMSG textbooks provide adequate extracurricular study?
Context: I'm a Grade 11 IBDP student and very fond of math. Assuming that I get the spare time to self-study material alongside the syllabus, I wish to spend it constructively (the only step I've ...
5
votes
2answers
121 views
Introductory book or other resource on $p$-adic numbers/number theory/analysis
I am having problems understanding $p$-adic numbers/$p$-adic number theory/$p$-adic analysis. I have tried some notes on the internet, but these notes were not helpful.
Can anyone suggest a book, ...
1
vote
2answers
119 views
What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?
I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
1
vote
1answer
42 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
votes
1answer
147 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 ...
3
votes
4answers
198 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 ...
2
votes
1answer
105 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 ...
20
votes
5answers
2k views
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
votes
1answer
92 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 ...
5
votes
2answers
587 views
Textbooks for an independent study in point-set topology
I am planning to sign up for an undergraduate "course" in point-set topology next semester. It is really an "independent study" in that this course will not have any lectures. It will just have two ...
4
votes
2answers
137 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+...
12
votes
2answers
157 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 ...
6
votes
1answer
96 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) ...
8
votes
3answers
197 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 ...
8
votes
4answers
236 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 ...
3
votes
2answers
317 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,...
3
votes
6answers
239 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 ...
3
votes
2answers
159 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 ...
5
votes
2answers
219 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
3answers
815 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
vote
1answer
109 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
votes
2answers
429 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
110 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
votes
5answers
269 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
votes
2answers
140 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 ...
9
votes
3answers
682 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
votes
2answers
194 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
148 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
votes
2answers
120 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
vote
1answer
105 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, ...
1
vote
0answers
116 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
votes
1answer
274 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 ...
14
votes
4answers
382 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
votes
3answers
253 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
votes
4answers
280 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
votes
3answers
229 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
votes
0answers
188 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 ...
7
votes
2answers
251 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 ...
13
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 ...
8
votes
2answers
403 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
votes
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 ...
5
votes
1answer
159 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
votes
0answers
113 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
votes
4answers
323 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
198 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
179 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 ...
