Hallo hallo TL! This summer I want to work on math, and in general I just want to keep a good stock of books handy for whatever occasion. I know math alright, but I really want to solidify my knowledge and work through all the maths again. Next year I want to try and tackle game theory, but in order to do that my math skills need to improve quite a bit. I also want to learn physics a bit more, but again, need to brush up on my more basic math.

So what I'm looking for are the following:

- GOOD Geometry textbook
- GOOD Algebra textbook
- GOOD Trigonometry/Precalc textbook
- GOOD Calculus textbook

Ideally, a "GOOD" textbook will cover all the main topics, have good explanations, good examples, and plenty of practice problems.

I work at my high school, but I think the text books there are horrible. Also, I'm not a huge fan of the Calc and Precalc book I used at UCSD, so give me some suggestions on good books to get!

Thanks TL!

illu

Canada2531 Posts

June 19 2010 07:07 GMT

I don't think Game Theory uses any of the topics you mentioned above.

Anyways, at University of Toronto, the standard calculus book is by James Stewart. He also has another book on pre-calculus. You should be able to pirate these off someone easily.

If you want to learn physics, it might be better to learn some linear algebra. A pretty simple and well-written book is by Fraleigh and Beauregard. The one by Kolman and Hill is OK too.

These will take you.... at least 6 months to learn properly. If you are still motivated by then, learn vector calculus. Marsden seems to be pretty popular, but I can't promise its readability.

Gatsbi

United States1134 Posts

June 19 2010 07:09 GMT

Game Theory is mostly Probability/Statistics and a little bit of Calculus.. I took it at UCSD.

illu

Canada2531 Posts

June 19 2010 07:13 GMT

On June 19 2010 16:09 Gatsbi wrote:
Game Theory is mostly Probability/Statistics and a little bit of Calculus.. I took it at UCSD.

That's what I thought, too. The topics OP had in mind are too rudimentary.

Gatsbi

United States1134 Posts

June 19 2010 07:15 GMT

And if Herb Newhouse is teaching it, I recommend waiting till another quarter, that guy sucks at teaching and it's not one of the easiest econ classes.

sOvrn

United States678 Posts

June 19 2010 07:24 GMT

Instead of books, maybe video lectures can be helpful to you. I know my little sister had a great experience using videos from the teaching company. They are pricey (around $100 or less) but worth the investment.

I bought one of the lectures on economics and thought the teaching style was superb, although the professor changes according to lecture. Google: the teaching company.

Empyrean

17067 Posts

June 19 2010 07:42 GMT

Get a good linear algebra book, a calculus-based probability book, a statistics text (won't be using this much), and a book that touches on discrete mathematics and maaaaybe some analysis.

You're not going to be learning game theory with only up to calc 2 lol.

Edit: By calculus-based I mean past the level of third semester calculus (basic vector calculus...think things like Stokes' Theorem and shit taught at universities).

crumunch

United States54 Posts

June 19 2010 08:30 GMT

http://www.artofproblemsolving.com/Store/index.php

I'd say these books are probably some of the best out there.

However, I think that their Calculus book only goes up to what would be considered Calc II. But in general all of these books are aimed towards those who really want to understand what they're learning, instead of just memorizing.

Caller

Poland8075 Posts

June 19 2010 08:34 GMT

afaik we have two game theory courses

one is pop game theory and requires basic stat and calc

the other requires real analysis

choose wisely

Plexa

Aotearoa39261 Posts

June 19 2010 08:38 GMT

#10

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2005/video-lectures/

Amazing series of lectures on linear algebra, although not a text book, should help solidify concepts (and is just generally really interesting!).

excelZerg

Canada69 Posts

June 19 2010 08:39 GMT

#11

have you looked at the stuff at http://www.khanacademy.org/ ? not textbooks but its a bunch of short instructional videos on a variety of subjects ive only looked at a handful of them so im not sure if he goes to the depth that you would want but it might be worth checking out.

Fifthman

United States11 Posts

June 19 2010 08:49 GMT

#12

I agree with illu; a good reference text specifically for calculus would be Calculus Early Transcendentals by James Stewart. It covers all the topics needed up to third semester calculus, and gives a variety of problems for each given topic. Some copies include a very handy set of cheat sheets which contain derivative and integral tables as well as trig tables.

If you're looking to learn physics, the text I like to use is Physics for Scientists and Engineers by Serway. It'll cover most calculus based lower division physics. If you're looking to stretch your legs a bit further into classical mechanics, look up Classical Dynamics of Particles and Systems by Thornton and Marion, although I wouldn't recommend this particular book until you understand multivariable calculus. If you're looking for other good physics resources, look up http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html for a quick reference page.

For linear algebra, Kenneth Kutler's pages look pretty helpful. The linear algebra notes in particular look promising. http://www.math.byu.edu/~klkuttle/0000ElemLinearalgebratoprint.pdf

If you're looking for something more basic in the precalculus realm, look up Wesner's Intermediate Algebra with Applications and Trigonometry with Applications. The examples look great, and each section contains a variety of problems.

Also, it may go without saying, but Wikipedia frequently has useful references to look up while doing problems. I personally learned more from Wikipedia than from the textbook I was assigned in freshman year for basic mechanics.

Av4st

Canada92 Posts

June 19 2010 11:34 GMT

#13

I highly reccomend using this book. It covers everything important from arithmetic (skip this part lol) all the way to calc 3 / basic linear algebra / basic probability

http://www.amazon.com/Engineering-Mathematics-K-Stroud/dp/0831133279/ref=sr_1_1?ie=UTF8&s=books&qid=1276941960&sr=1-1

It's a pleasure to read because it explains things extremely clearly and concisely. Another plus is that it focuses more on examples rather than long convoluted definitions, which I believe is a HUGE flaw in how other math textbooks are layed out.

It helped me go from being a grade 11 c average highschool dropout(although mainly due to sports), to a 4.1 gpa comp sci / math university student.

Cloud

Sexico5880 Posts

June 19 2010 12:08 GMT

#14

The calculus by Louis Leithold pretty much covers everything in your list.

Cloud

Sexico5880 Posts

June 19 2010 12:12 GMT

#15

On June 19 2010 17:38 Plexa wrote:
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2005/video-lectures/

Amazing series of lectures on linear algebra, although not a text book, should help solidify concepts (and is just generally really interesting!).

The 2 books written by that author (Strahm?) on linear algebra are the best there are. One of them covers a little of game theory (not the one used in the course).

Cloud

Sexico5880 Posts

June 19 2010 12:15 GMT

#16

If you want hardcore maths, try Russian authors like Piskunov.

Muirhead

United States556 Posts

June 19 2010 13:12 GMT

#17

It sounds like you want mainly high school math?

Artofproblemsolving would be best for you in general. If you want trig go with Trigonometry by I.M. Gelfand. That book was my bible at the end of 7th grade.

Only you know what prereqs your game theory course actually has, but I would look into that before studying absolutely everything.

If you don't want to spend lots of $$ (i.e. you don't want to spend any), and you just want to brush up on basic high school math, try doing old AMC 10/12s from art of problemsolving contests sections and reading the solutions.

Plexa

Aotearoa39261 Posts

June 19 2010 13:36 GMT

#18

On June 19 2010 21:12 Cloud wrote:

Show nested quote +

The 2 books written by that author (Strahm?) on linear algebra are the best there are. One of them covers a little of game theory (not the one used in the course).

The lecturer is Gilbert Strang

(he was at my uni the other day giving a lecture on triangle spaces - was pretty funky haha)

zeuS~

United States193 Posts

June 19 2010 14:09 GMT

#19

http://www.youtube.com/user/patrickJMT - this guy does tutorials on calculus and alg. using this to refresh my calc for when I go back to school in the fall ^^

Rev0lution

United States1805 Posts

June 19 2010 14:39 GMT

#20

A good calculus book that I've been reading, and by god, is it explained beautifully is Calculus with Analytic Geometry by Sherman Stein.

http://www.amazon.com/Calculus-Analytic-Geometry-Sherman-Stein/dp/0070611750

Amazing.