# I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff

Next week, I'm beginning the 2nd semester of 9th grade in the country's leading Comp Sci High School. (the profile is actually Math-Comp Sci, but this HS focuses more on Comp Sci, whereas other ones focus more on math). What I did in grades 5th-8th (and that I should know almost perfectly) is from natural numbers (5th, arithmetic) all the way to linear equalities and inequalities, 2nd degree equations (8th grade) with a dash of plane and some 3D geometry. Judging by the results of my HS admission test, I should know these things pretty well, but it seems to me as if I don't have a good grasp (I'm getting rusty, or in fact never been that good). Now, in the 9th grade, it happened that I have the worst math teacher in the entire high school (other teachers complain about him, from the ones that teach Comp Sci to the geography ones, all the students complain about him). He just comes in class, writes the basic definitions of something, shows us no practical examples (well, not practical, but how to solve the exercises involving them) and he gives obscene amounts of homework (I checked with other HS math teachers).

So, basically, what I need is this: something that I can study on my own (so, a book with examples, lots of exercises in the entire difficulty spectrum and solutions would be great) to get a really firm grip on basic geometry (similar triangles, Pythagorean theorem, the really basic stuff), the algebra from 5th-8th (including the arithmetic parts, like properties of $a \vdots b$ then $a \vdots nb$) and then a good resource for the highlights of high school (so I can get a good grip of what I currently should be studying, but can't because of the poor teacher), plus the stuff from higher years (logarithms, complex numbers etc.). Why I'm asking this question? Because I decided I want to learn Real Analysis, and found that while I understood all the concepts, I couldn't handle the exercises and I had difficulties with the rather basic stuff (linear eqs. and so on).

Sorry if the location isn't quite right, but this seemed like the best place to ask this question.

Any good books, or resources, or stuff I should look into, or a list of things I should have a really good grip on before moving on to more advanced stuff. Any suggestion is appreciated.

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Have you tried the prescribed textbook? They tend to be fairly thorough regarding the material you need to cover and often introduce some other new more advanced topics at the end. – E.O. Jan 11 '12 at 8:47
The teacher (though I'm not sure of how much to rely on his opinion) said that it's no good, because it's really old, and it's been modified over time in order to match the new curriculum, and now it's a potpourri of stuff, not very useful for learning. From what I've seen, it's quite comprehensive on the theoretical side, but offers almost no exercises and no indication on how to do them. And, even it were good it only covers 9th grade. I need a recap on older stuff, and I also need more advance stuff (trig, and other analysis pre-reqs). Thanks for taking the time to answer. – andreas.vitikan Jan 11 '12 at 8:56
Speaking from my own experience I have found the IB HL textbook (amazon.com/Mathematics-International-Students-Dipolma-Core/dp/…) very helpful. Assuming you want to learn real analysis you probably want to get calculus down in the process too before you get started which would require you to be pretty solid in the basic stuff first. However the book I mentioned is pretty expensive, so a guideline on how much you are willing to spend would be good. – E.O. Jan 11 '12 at 9:04
Thanks for the recommendation. As for spending, anything within reason is OK. I could afford, maybe 3 or 4 textbooks like that. Also, free resources are more than welcomed (but from personal experience, good ones are hard as hell to find). In fact, that book looks more or less like what I'm looking for. I'll find a way (maybe look over the old notebooks) to get a proper grip on 5th - 8th algebra, and paired with that book I should be set (it seems to have sequences, trig, functions and the works). And it's for the International Baccalaureate ? Even better then. – andreas.vitikan Jan 11 '12 at 9:12

I suggest beginning with the Gelfand School Outreach Program books by Israel M. Gelfand. These are easy to find at amazon.com and they are not expensive.

Gelfand/Shen -- Algebra

Gelfand/Glagoleva/Shnol -- Functions and Graphs

Gelfand/Glagoleva/Kirilov -- The Method of Coordinates

Gelfand/Shen -- Trigonometry

Also, there is a huge number (many hundreds) of possibly appropriate older books that you can find digitized on the internet. For example, the following book is very well written and it appears to contain much of what you are looking for:

Charles Smith, Elementary Algebra (1890)

Here is another example:

John Henry Robson, An Elementary Treatise on Algebra (1875)

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Khan Acedemy is getting positive reviews for self-study using its approach of short videos and a lot of practice.

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Thanks for the reply, but I have tried learning from KhanAcademy and I can't. It's just not my style. Either having someone explain it to me face-to-face or using a book, because it's either a faster pace or -in the case of a book- I can set my own pace. However, I could learn the stuff from some other source, ideally written, then do the practice there and maybe even use it as a list of things to go through. So, thanks for the suggestion. – andreas.vitikan Jan 11 '12 at 8:31
+1; I have always wanted to study some chemistry, but I never thought that the occasion to do that would have come from Math.SE! – Giovanni De Gaetano Jan 11 '12 at 14:47
You can watch the videos over and over, or stop and back up at any time, so saying it's too fast paced seems not quite true to me. – Graphth Jan 11 '12 at 15:24
@Graphth: when I read the OP's comment I thought he was complaining that Khan Academy goes too slowly (that face-to-face has a faster, and hence preferred, pace than online videos). But upon re-reading it after seeing your comment, it appears that either interpretation could be drawn. – Willie Wong Jan 11 '12 at 16:38
@WillieWong Yea, I guess I don't know for sure. – Graphth Jan 11 '12 at 16:42

The Art of Problem Solving has a bunch of books starting at Prealgebra, going all the way through Calculus. And, included in these are topics a typical high school student might not see, like counting and probability, and number theory, both of which are useful to people studying computer science. And, there is a geometry book. The books are very reasonably priced and you can buy full solutions manuals along with them. The solutions manuals are very inexpensive if you buy them with the corresponding book, i.e., you get a discount for buying them together. And, beside having the main topics, these books try to teach problem solving skills.

http://www.artofproblemsolving.com/index.php?mode=books

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I haven't looked at the Schaum's Outline of Geometry, but usually the Schaum's Outlines make a good source for self-study. The Schaum's Outline of Precalculus I think would help in your preparation in learning higher mathematics also. You usually find some explanation and plenty of solved examples/exercises in a Schaum's. The REA Problem Solvers series might also help, as there exist plenty of solved problems there also.

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When preparing for Calculus the website of PatrickJMT really helped me out:

http://patrickjmt.com/

There's an insane amount of free math videos on there that are extremely easy to follow but go into quite some depth. Enough to help me trough my Bsc in Computer Science. Just be sure to pause the videos often and trying to solve the equations before he shows you how it's done.

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Why did this get downvoted? – Graphth Jan 11 '12 at 15:26