## CSETMathGuru: THE Site for Single Subject Math

**What texts/resources should one use for Subtest I**

**Number Theory / Abstract Algebra?**

Subtest I consists of Precalculus-level Algebra as well as Number Theory & Abstract Algebra, the most worrisome aspect of which is the latter! I imagine some Math fellow at NES - those are the chaps that devise these Qs - sitting somewhere cold and inhospitable, rubbing his hands in sinister satisfaction, titillated that his Abstract Algebra questions offer the most insurmountable obstacle to the candidates...!

Here's my humble opinion (Gawd, how I hate that phrase!): there are just about 3 or 4 MCQs on those topics (Divisibility of Numbers, Groups, Rings and Fields, etc.) and perhaps 1 Q in the Free response section. If I were you, I just wouldn't bother! What I recommend is to make very educated guesses on those questions, but NOT waste precious time preparing diligently for them and trying to 'grasp' those concepts this late in the day! It's simply NOT prudent!

First, in Subtest I, there are far more important and infinitely more accessible topics - like 'regular' Precalculus stuff - that you can REALLY do well on! In my own CSET attempt - having majored in Mathematical Statistics, I took all 3 Subtests together, and passed most comfortably! - I examined Qs from those abstruse topics (they are usually Qs 1-3 in the MCQ section, and Q1 in the Free Response) only at the the very end, when I had devoted my best energies on the others items, and had time to dissipate!

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And I was certain that of the ~ 26-27 Precalculus-Algebra questions, I'd got 90%+ of those absolutely nailed down!! Further, in ALL my teaching experience - I've taught the gamut of High School Math levels and subjects - I've never had to make reference, even tangentially, to an Abstract Algebra or obscure Divisibility concept! I suppose it'd makes sense to study them if it was indeed likely that you'd apply them in class.

Finally, if you're like most examinees, you have very limited time resources! Would you rather expend it on matter that you definitely OUGHT to know, and that is easily self-teachable OR would you break your hand on something you shall probably never encounter, even when utterly sozzled at a bar?!

So, my take on this issue is that you'd profit tremendously by simply directing your efforts towards the more comprehensible Precalculus portions of the test, and simply give Abstract Algebra/Number Theory the heave-ho! You are all but assured of 1 question on Mathematical Induction, which topic I earnestly advise you to study and master!

But if you DO have the time, you might find the following texts useful:

1. Schaum's Outline of Group Theory

By: Baumslag/Chandler

Pub: McGrawHill

2. Schaum's Outline of Modern Abstract Algebra

By: Frank Ayres

Pub: McGrawHill

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