I’m taking a Calculus course this semester - classes begin next week. The professor emailed us the syllabus with all of the homework and readings we have to do week by week. I decided to get a head start on some of the readings/take notes/do homework, etc.
I have a pretty solid familiarity with Calculus through my AP Calc course in high school. All of the concepts I’ve gone over so far in the syllabus I’ve already learned in previous math classes. However, it seems like relatively simple concepts that I know quite well, like composition of functions, are explained in a way that is unnecessarily complex. When I read through that section (and reread through it… and re-reread through it), I can barely put 2 and 2 together. But then when I work on the practice problems, they’re all quite easy and I breeze through them. I’ve been watching Khan Academy all winter break and I’ve found that Khan Academy is rather casual and I have no trouble understanding the information/topic.
Are college math textbooks typically more rigorous than say, the professor’s lectures? I’m not a STEM major and this is the first and last math class I will be taking in college. Are math textbooks used as the primary source for learning? I’ve been taking detailed outline notes and I wasn’t sure if this was the norm or if people use textbooks just for practice problems/homework.
From what I’ve heard, most basic math students (Calc I/II) use the textbooks only for practice problems; I’d like to get another opinion on that though.
The irony is that I have a notebook full of notes from Khan Academy starting from Trig all the way to Integrals and it all seemed really simple - and now I just finished an outline of Chapter 1 in my textbook and it is like, unnecessarily verbose and provides far more nuanced, rigorous definitions. There was 4 pages dedicated just to what a piece wise function is.
It varies a lot from book to book. Some math textbooks are beautifully written, and others leave quite a bit to be desired. As a physics major, I’ve taken quite a bit of math. In my experience, the professors lectures serve as the primary education tool. The textbooks serve as supplementary reading for the most part. When I work through homework or practice sets, I tend to reference my notes far more than the book.
Is there a reason that you are retaking what you learned in AP calculus? Did you try the college’s old final exams for this calculus course and find that your knowledge of the material is weak?
@ucbalumnus - I received a 3 on the AP exam which doesn’t garner credit at my school. I don’t necessarily think my score is indicative of my knowledge of Calculus - I took it at the end of my senior year when I had basically mentally checked out, so to speak, of high school, but overall, I was a very strong Calculus student. I did find the final exam from last year (they are standardized amongst all Calculus sections/professors at the university) and everything seemed to click - there wasn’t anything I wasn’t familiar with/couldn’t work through, etc.
Some textbooks are a bit over convoluted for the class for which they’re assigned. This is probably especially true for introductory calc classes. Most classes, including math classes, the book will be appropriate for the class, but there will definitely be a number of exceptions you’ll see through undergrad.
My professor said that college textbooks are written by professors for professor. I personally thought they were written poorly on purpose to weed-out students. Take your pick.
I have personally completely stopped reading my textbooks and rely entirely on youtube and the internet for knowledge. I 2nd @Vctory and practice problems are the only use for a textbook.
For Calc 1-3 I highly recommend Professor Bruce Edwards from The Great Courses (when it’s on sale for ~70 dollars)
Math textbooks tend not to encapsulate essential concepts,and end up being rather verbose tomes. They are written mainly for professors because they make the adoption decisions.Overly student friendly textbooks are viewed as “not rigorous” or “dumbed down” by professors.
What ends up happening is that most students use the book for just problems, and look to YouTube or Coursera or EdX for video help. I encourage all my students to be familiar with the concepts outlined in the text, and when I select texts for my courses, readability is number one on my list. Sometimes the textbooks are chosen by committee and an individual professor may be “stuck” with teaching out of a hard to read book.
I completely disagree with what most have been saying at least for the couple of introductory calculus and physics books I’ve used. There are a few that are just awful calculus textbooks for beginners but I thought Stewart’s was pretty well constructed.
The main thing is that a math textbook has to tread a very careful line because the writers know that they have to be accessible to non majors (like yourself), engineers (who mainly only want to know how to solve problems and apply), and math majors (who are looking for rigorous treatment of the subject). I think most tread this line as well as possible. by treating their books in ascending order where they treat the concepts first then the most basic examples then complex examples then rigorous math theory and proofs are at the end for math majors.
Another thing about math is that it is very specific because one little change in notation or description can make your result horribly inaccurate. This is why they use very specific symbols and phrases to define the concepts in the book. It’s not so much convolution as much as a need to be specific.
I never found any calculus text overly convoluted as an engineering major, but Stewart’s calculus was above and beyond much more beautiful than the others.
As mathprof63 said, you can also now look up all the concepts up on youtube. Between khanacademy, integralcalc, and patrickjmt there will be very few if any gaps in your calculus knowledge and all of the concepts are explained in a way that a non major could easily grasp.
@jimmyboy23
Stewart is a total POS calculus textbook. I found an ancient 1970s calculus textbook in the student center that was better written than that junk. It was more rigorous and easier to read if you can believe that. IMO Stewart is the epitome of convoluted garbage. I took calculus for an entire year with that textbook, received As, and proudy state that I never read a single page of that textbook.
good textbook was called: The Calculus with Analytical Geometry Harper & Row circa ~1970
@guineagirl96
What beauty? The fact that @jimmyboy23 recommends “khanacademy, integralcalc, and patrickjmt [to fill in] gaps in your calculus knowledge” is a testament to the inadequacy of that textbook.
@bomerr that’s not the fault of the textbook. That’s a student who needs a different type of learning to understand. All those methods have lectures that involve problems and examples written on the board, which helps draw connections which you may not make by just reading it out of the book. I always found lectures helpful too.
Trust me, I’ve had horrible text books. Stewart is not one of them.
@guineagirl96
I found everyone in my calculus class who got As at most used Steward purely for practice problems. No one read his convoluted explanations and instead relied on better sources such as PatrickJMT. Clearly that is a testament to the gross inadequacies of his textbook. The amazon reviews confirm this with an average rating of only 3 stars. Reviews say:
I didn’t mean to start a publisher war, lol. I guess my question had more to do with what the general nature of Calc I classes were - whether the material is primarily presented in lectures or if students self study from the textbook.
I also hate Stewart’s calculus textbook. It was so convulated and confusing! It didn’t help me at all - after a while I stopped using it except to do the homework problems. I used an intro to analysis textbook to fill in the gaps with proofs (I did honors calculus, so there was quite a bit of this), and my AP prep book from high school for the basic stuff/applications. My professor hated it too (only used it because she was required to by math department).
I much preferred my high school’s textbook for calculus (Thomas’ Calculus: Early Transcendentals). It was so much easier to understand.