# Self study topics and material for mathematics

by kamykazee
Tags: material, mathematics, study, topics
P: 867
 After Algebra 2 (which would cover some trigonometry) should i go for a more thorough geometry course or go into Pre-calculus and afterwards into Calculus? Should i tackle any other subject before Calculus?
Well, I'm an engineering student currently in a differential equations class (think the next step beyond calculus), and I've never taken a geometry course. Occasionally I miss it, but most of the axioms are just that: common sense. I think you could safely skip geometry and not miss anything. I also think you'll do fine with just algebra I/II and precalc/trig.

 Another point i would like to put forward is - after Calculus, which subject should i tackle and could someone recommend any textbooks or materials for it?
Depends on what field you're going into. If physics/engineering, the next step is ordinary differential equations. I've only ever delved into one textbook on ODE's, but I've found Boyce and Diprima's Elementary Differential Equations to be quite satisfactory. It was good enough that I was able to get a head start in my class over the summer. You don't need the newest edition, so you can find a very cheap copy online. I also recommend going to Khan Academy. He has a way of explaining what's going on behind the scenes that really helps with understanding the material.
 P: 5 Thank you for the reply. I've edited the initial text in the hopes that my situation is better expressed in this way. I'm not sure on a particular field at the moment, as i've said i'd just like to understand more about it at this point.
 P: 219 Self study topics and material for mathematics hi for going beyond calculus i suggest first taking a course in linear algebra as it is used in many areas of higher mathematics and it is good to be acquainted with its ideas. if you haven't already you definitely should learn multi-variable and vector calculus (calculus III) along with linear algebra as they go hand in hand. Once you learned these subjects which are usually courses a first year mathematics major would take you can really go dive into many other subjects. If you are interested in the more applied side of math you can try ordinary differential equations. The book by boyce and diprima is not the best but it should give you a decent grounding in the techniques. however if you want true understanding and not just memorizing techniques you may want to pick up another book such as vladimir arnold's ordinary differential equations. if you want to go more on the pure side, you can go into abstract algebra, real analysis, or topology to name a few. these are proof based classes however so if you are not familiar with reading, understanding, and writing formal proofs it may be good to take a proofs class which is usually called introduction to mathematical reasoning or something similar to that. if you have the proper foundations and a willingness to work hard then these courses are definitely within your reach.
 P: 5 Yes well, the problem is i don't have the option to take such courses. Hence i rely on books/textbooks explaining these. :) Could you point me to some explaining mathematical reasoning? And yes i am interested in actually understanding and not merely memorizing. I would prefer if suggested reading/materials and textbooks would favour a proper understanding.
 P: 219 well one choice for multivariable calc and linear algebra is "Linear Algebra, Vector Calculus, and Differential Forms" by John Hubbard. it gives a unified approach to these concepts and is very rigorous and focused on understanding rather than simple computation.
HW Helper
P: 1,347
 Quote by kamykazee Here are the textbooks i've decided upon after some browsing on the internet: Algebra I: Expressions, Equations and Applications, by Foerster Geometry, by Jacobs Algebra and Trigonometry: Functions and Applications, Foerster
Personally I'm not a fan of Foerster:
- The explanations aren't as clear as I liked.
- I find a disconnect between the instruction in the book and the harder problems.
- There's no color in their diagrams/photos/illustrations.
- I don't like the method presented in teaching word problems.

If I were you, I would instead get the Algebra books by Lial:
- Introductory Algebra, 9th ed. (ISBN-13: 9780321557131)
- Intermediate Algebra, 9th ed. (ISBN-13: 9780321574978)
These are "self-teaching" texts -- the teaching is in the examples. I have these, and if I wasn't too late with the textbook forms at my high school, I would have adopted them in my Algebra classes.
 Mentor P: 18,345 Why not go for the decent math texts?? Try "basic mathematics" by Lang. It covers everything in algebra and geometry. And it's a text that isn't dumbed down at all.
 P: 5 Well there seem to be some diverging opinion - one vouching strongly for Lial and the other for Lang. I have managed to actually see a preview on amazon of Lang's book and it seems pretty good. He seemed to explain in a good manner, as in he tried to make you understand why this notation is this or why this is the way it is, not just slap it in front of you. Cheapest one i could find was about 25$. About the Lial ones - i found some of the seventh edition for only 5$. I think they should be the same or nearly the same content-wise?
 P: 183 I don't understand why you are worried about materials for advanced classes, when you are still learning the basics. It will probably take you at least a couple of years before you are ready for, say, differential equations. If you waste time looking for a book on that now, not only will you be taking time away from study, but you might end up buying something that you won't use, because something better will have come along by then. For example, look at this course for self-study in calculus: http://ocw.mit.edu/courses/mathemati...lus-fall-2010/ That's probably the best course you can find today for first-semester calculus. It's free, it's from MIT, it is written especially for home study, it has all the video lectures and class notes and homework and exams and solutions. It's perfect for you. And it didn't exist two years ago. Who knows what will be available two years from now? So just take your classes one at a time, and then see what's best for your next class when you're ready for it. And to answer your question about precalculus books, I like this one: http://www.amazon.com/Precalculus-Ma.../dp/0534492770 Pretty hard to beat for ten bucks (used).
 P: 5 As i said, i have gaps - some material i cover quickly as i already grasp, some (where the gaps are) i cover slower. Thanks for the MIT link aswell the pre-calculus recommandation! I think you are correct, however, there will be awhile, atleast months, until i start calculus. Thanks for the advice.
 P: 67 I too recommend Precalculus - Mathematics for Calculus by James Stweart. It is a great book. Older editions should be available quite cheap second-hand.
P: 207
 Quote by Angry Citizen Well, I'm an engineering student currently in a differential equations class (think the next step beyond calculus), and I've never taken a geometry course. Occasionally I miss it, but most of the axioms are just that: common sense. I think you could safely skip geometry and not miss anything. I also think you'll do fine with just algebra I/II and precalc/trig. Depends on what field you're going into. If physics/engineering, the next step is ordinary differential equations. I've only ever delved into one textbook on ODE's, but I've found Boyce and Diprima's Elementary Differential Equations to be quite satisfactory. It was good enough that I was able to get a head start in my class over the summer. You don't need the newest edition, so you can find a very cheap copy online. I also recommend going to Khan Academy. He has a way of explaining what's going on behind the scenes that really helps with understanding the material.
While I agree with the second half of your post, I do not agree with the Geometry half.
A rigorous study of Geometry will not only help develop "mathematical maturity" (I always find this phrase a little funny), but will also give you tools in identifying symmetries and structure in Physics and Engineering. Geometry is a great way to understand many of the key topics in physics (perhaps the most obvious being GR). Geometrical intuition is something that everyone could use if they plan on having a deeper understand of the Physics they are working on (though I'm less familiar with Engineering topics, I'm sure it couldn't hurt).
While Geometry isn't *necessary* to be come good at the calculation based work (Pre-Algebra through Diff Eqs), it's necessary for (what my professor consider) the first "real" courses, like (Linear Algebra upwards).

**I'm not arguing that there isn't real math in Diff Eqs or Calculus, it's not my place to, but I think it's safe to say that there is more substance to the higher-level, abstract material**

Just my thoughts,
Elwin

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