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Academic Guidance Academic Guidance - Academic guidance for those pursuing a college degree... what college? Grad school? PhD help?


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October 18th, 2012, 06:40 AM   #1
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Please suggest textbooks for high school math.

I am a 19 year old high school drop-put. For some reason, I cannot pursue higher studies. I have studied till the 10th grade and always loved math. I have always maintained an A in math, without much effort since we all know its not difficult. More importantly I loved doing math. Can I study till graduate level only through textbooks and the internet? Is a teacher necessary? Thanks. Sorry if my question has already been asked as I am new to the forum.
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October 18th, 2012, 07:23 AM   #2
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Re: Please suggest textbooks for high school math.

Graduate studies are hard, but cross that bridge when you come to it! You can surely learn the rest of high-school math and much of undergraduate college math on your own, with some dedication.

We've collected some math resources here
viewtopic.php?f=56&t=23165
which you may find useful. Some are good for your present level (Khan Academy), others for later in your studies (MIT OpenCourseWare), and a few for all levels (OEIS).
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October 20th, 2012, 07:00 AM   #3
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Re: Please suggest textbooks for high school math.

Thanks a lot. But do you have any textbooks to suggest?
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October 20th, 2012, 09:21 AM   #4
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Re: Please suggest textbooks for high school math.

I don't -- I'm not very familiar with high-school math. But I've moved the thread to the Studying & Teaching Math forum where I hope others will respond.
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October 30th, 2012, 10:50 PM   #5
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Re: Please suggest textbooks for high school math.

I’m a big fan of Reid’s “Undergraduate Commutative Algebra” and “Undergraduate Algebraic Geometry” which are both very accessible (moreso than Eisenbud, which is rather intimidating) and work very well together. Also, Cox, Little and O’Shea’s “Ideals, Varieties and Algorithms” assumes…nothing. It doesn’t assume you know what a ring is or anything, and approaches algebraic geometry very much from the point of view of solving polynomial equations, which is helpful for someone in high school.

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October 31st, 2012, 06:53 AM   #6
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Re: Please suggest textbooks for high school math.

Math at the upper undergraduate and graduate levels is a very different beast than it is in high school. In particular, the material becomes less about computation and more about proving things. Basic coursework (classes like calculus and introductory linear algebra) you may be able to do on your own easily enough (one of the biggest barriers will be actually keeping up on your work--without deadlines and people to keep you accountable, it can be difficult to see things through), but once you transition to actual math courses (real analysis, abstract algebra, number theory, etc.), instruction really is beneficial.

While picking up many of the main ideas is possible for a (very) motivated student to do on their own, it is difficult (and vital) to understand when you have made mistakes in your own proofs. I think it is very difficult to actually understand introductory proof based courses unless you have someone to actively critique your work. Mathematics is an incredibly subtle art and a large part of the initial learning process is to go back and understand your mistakes, but being able to detect mistakes in your own work requires being at a level that takes many people years of study to achieve.

At any rate, I will put forward my usual recommendation for a starting book, Lang's Basic Mathematics. It is a more challenging (and proof preparatory) treatment of the math you need to know from before calculus.
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January 2nd, 2013, 11:16 AM   #7
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Re: Please suggest textbooks for high school math.

It should not be very difficult if you have a solid understanding of what you learned so far. Now a days with plenty of online lectures this should be even easier. Go to the open courseware for great math lectures.
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