EPTMath textbooks! - Page 2
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Sirakor
Great Britain455 Posts
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Xeris
Iran17695 Posts
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FiBsTeR
United States415 Posts
On June 19 2010 17:30 dig wrote: 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. This. I helped the authors of these proofread some of their books and they are extremely well-written. Tons of "good", unique problems, not like normal textbooks that are just a handful of types of boring problems copied and pasted with different numbers. EDIT: So just to clarify, these books intend to (1) teach the basics of algebra/geometry/combinatorics/number theory/calculus and (2) apply this small set of tools to solve beautiful problems, mostly in the context of high school math contests. Most high schools just do (1) but not (2)... it's like telling someone how to hit a nail with a hammer but not saying why you would ever want to do so. Also, there is a really nice book by Paul Zeitz about problem solving that takes a step back and looks at various overarching strategies of how to approach a (math) problem mentally. I always thought it was like teaching the metagame of math contests but I might get in trouble for saying so. :X | ||
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Muirhead
United States556 Posts
By the way Xeris you can never "master" high school math. Try the problems here  :http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=2009&sid=664e786a7cdebc8f0f76a00ffdfe3fd4 | ||
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Xeris
Iran17695 Posts
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mdainoob
United States51 Posts
The idea is that applying what you've learned to different problems that you haven't seen before can help solidify that knowledge. For the purpose of getting a more solid foundation in high school math + calculus 1/2, I guess it depends how familiar you are with the material. If you can do the basic computations very well (stuff like factoring, doing easy derivatives/integrals, solving trig equations, etc...) see if you can understand the reasons behind why certain things work. For example, you might be very good at using the quadratic formula but do you how to derive it? Or you might use the fact that loga + logb = logab but where does that come from? Or the fundamental theorem of calculus, why is it true? Or maybe you use the chain rule a lot but do you know why intuitively it makes sense? By investigating why certain facts you take for granted are true you can also gain a better understanding of the material. Point is that reading over book explanations and doing standard exercises can help but doing different problems (as opposed to doing the same ones over and over again) or investigating things is also important to solidifying the fundamentals. For calculus, I like spivak's book but it might be a little tough. | ||
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theonemephisto
United States409 Posts
EDIT: Didn't see it was mentioned above. | ||
SultanVinegar
United States372 Posts
+ Show Spoiler + and if you have a kindle or don't mind reading from your computer, it's really easy to find on the internet | ||
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qrs
United States3637 Posts
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Lyriene
United States346 Posts
On June 19 2010 17:30 dig wrote: 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. +1 for this book. The explanations are really clear and the problems are rather difficult compared to other books. I agree with dig that these books focus mostly on concepts rather than formulaic solving. | ||
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Oxygen
Canada3581 Posts
As for an algebra textbook, I don't know whether you mean abstract algebra or linear algebra. You've got tons of good resources for linear already available. MIT LECTURES ARE AWESOME - as well as many other online lectures found on YouTube and other sites. So here's a great book for anyone wanted to teach themselves group theory and eventually Galois Theory without any knowledge of abstract algebra whatsoever: Abstract Algebra and Solutions by Radicals by John E. Maxwell and Margaret Maxwell. I've actually been looking to tutor a lot of math this summer but haven't managed to find many students. I like to really understand concepts in math and find the simplest explanation possible, so if you have any questions, I would love the challenge of explaining! Let me know and I'll send you my email. EDIT: BTW, the desire to truly master and fundamentally understand things is excellent for mathematics! Math is like a really long linked chain (with branching). When you are doing a proof, you are checking one link in this chain -- you're not proving many of the things that came before that, or many of the things that come "after". You're not constantly reproving that x + 0 = 0 + x = x, for instance. Ask yourself the question "but why?" and "can I prove this?" continuously, and take the time to just noodle around with different equations and stuff. | ||
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vesicular
United States1310 Posts
I'd say Calc isn't all that applicable unless you're doing game programming (note this is different from game theory). | ||
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Xeris
Iran17695 Posts
On July 03 2010 00:14 Oxygen wrote: I really like Stewart for Calculus, I find most of what I need there, though some of the proofs are omitted and that kind of sucks. As for an algebra textbook, I don't know whether you mean abstract algebra or linear algebra. You've got tons of good resources for linear already available. MIT LECTURES ARE AWESOME - as well as many other online lectures found on YouTube and other sites. Basic algebra... haha, nowhere near Linear Algebra and stuff yet T_T | ||
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kainzero
United States5211 Posts
BTW, take advantage of the fact that older editions are dirt cheap. I was the last class to use my edition, and the price plummeted online from $120 to something like $4. | ||
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Servius_Fulvius
United States947 Posts
I used this book for Calculus 4 aka Differential Equations. Out of my four semesters, I thought Diff-Eq was the least intense. The first chapter is especially helpful since it lays out how to solve basic, homogeneous, separable, and exact differential equations - things you're going to see a LOT when studying physics (Newtonian physics, that is...higher levels require a lot of vector calculus). I'm not that great with math, and with this book I was able to teach myself the material since my professor sucked. | ||
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Hidden_MotiveS
Canada2562 Posts
edit: Don't be too picky, just make sure it's in your library and not "just for kids" | ||
]343[
United States10328 Posts
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!). MIT OCW is awesome. On June 19 2010 17:30 dig wrote: 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. These are among the best for learning elementary, contest-y math [algebra, geometry, combinatorics (including game theory), and number theory]. (But still overrated!... since they're pretty much the only ones that comprehensive out there. Some people think of them kind of like a Bible... they're not quite that good  ) Algebra is the standard Algebra I/II stuff from high school, plus more tricky stuff like Vieta's formulae for polynomials, multi-variable inequalities [Lagrange multipliers = >  ], and such.Geometry is standard high school geometry, plus a lot of much more advanced stuff that is really cool but totally useless. I'm still bitter for spending so much time on that -__- Combinatorics is counting and probability, which is much harder than it sounds. Also, it's related to set theory, and whether some macroscopic facts about some set can imply certain structure, and vice-versa. Number theory is the study of integers: integer-solution (Diophantine) equations, factorization/divisibility, and lots more. Closely related to abstract algebra/group theory. On June 20 2010 03:08 Muirhead wrote: Zeitz's book is a little advanced, no? By the way Xeris you can never "master" high school math. Try the problems here :http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=2009&sid=664e786a7cdebc8f0f76a00ffdfe3fd4 lollll darn I wish I made MOP this year I haven't even solved the TST problems yet (and I've known them for like 2 weeks...)and Zeitz's book, The Art and Craft of Problem Solving (similar title ftw), is generally geared towards people preparing for the Putnam exam (the biggest/most prestigious (?) college math contest in the US). All of these have emphasis on proofs, in varying degrees. Earlier Art of Problem Solving books are simpler and not so focused on rigor, whereas more advanced books like ACoPS and harder AoPS books are. (And I'm pretty sure the OCW Linalg course is too, though I haven't finished it yet -__-;;; I probably should...) Ok I'm not sure how much of that was useful to the OP, but... my two cents for now XD | ||
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Xeris
Iran17695 Posts
Next question is: What kind of math do you need to know for modeling, and higher level statistical analysis. I'm leaning towards doing a PhD program in political science (FUCK I KEEP SWITCHING between that and law school, but I feel 70-30 now in favor of doing a PhD program) - and I will likely need to learn how do both modeling and analysis. What kinds of math does that involve and what's the best route to learn it? Since I'm taking next year off before I go to my grad program, I want to get as much of a head start as possible on that stuff, since it will probably be difficult for me. | ||
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illu
Canada2531 Posts
On July 03 2010 09:10 Xeris wrote: Thanks for all the feedback! Next question is: What kind of math do you need to know for modeling, and higher level statistical analysis. I'm leaning towards doing a PhD program in political science (FUCK I KEEP SWITCHING between that and law school, but I feel 70-30 now in favor of doing a PhD program) - and I will likely need to learn how do both modeling and analysis. What kinds of math does that involve and what's the best route to learn it? Since I'm taking next year off before I go to my grad program, I want to get as much of a head start as possible on that stuff, since it will probably be difficult for me. I think you either want to do a PhD in statistics, or work with someone who is specializing in statistics. I think it would be very hard for you to master both polisci and statistics at the same time. Remember you don't have to know absolutely everything - just work with someone that knows the stuffs that you don't know. Assuming you are focusing on polisci, knowing some of the basics of statistics really helps. This allows you to identify the problem at hand more easily so you know when you need to seek expertise. To that regard, I think if you can do almost everything on Moore's Introduction to the Practice of Statistics, it should be more than sufficient. IPS is non-technical, has no calculus or any other kinds of "hard" math in it, and will provide you with background on applied statistics. | ||
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Servius_Fulvius
United States947 Posts
On July 03 2010 09:10 Xeris wrote: What kind of math do you need to know for modeling, and higher level statistical analysis. I'm leaning towards doing a PhD program in political science (FUCK I KEEP SWITCHING between that and law school, but I feel 70-30 now in favor of doing a PhD program) - and I will likely need to learn how do both modeling and analysis. That depends on if you're learning the math behind the statistical modeling or just learning how to do a modeling program. PoliSci majors at the University I just graduated from don't need to take advanced math, the statistics are covered in an undergraduate course or as something extra. You can always check the program's class requirements online to be sure (since most colleges post this).However, in programs like Economics which deal HEAVILY in statistical analysis, they're required to learn single variable, multi-variable, and vector calculus and differential equations (calc 1-4). To be fair, I took an engineering statistics course my second year and all I really needed was single variable calc. | ||
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