Abstract Bracketology 1

Sorry for the delay in posting readers! I've been doing some construction work, which has been taking up a great deal of my time. I'm back with a possibly poorly timed application of mathematics to the world of sports.

Year after year my NCAA March Madness Bracket falls apart, and I've had enough. It's time to mathematize (this, rather than increasing my knowledge of college basketball, is of course the easiest way to improve my results). I'll be continuing my work on this indefinitely, as I've already come up with a number of interesting questions to look at. We start small, looking at strategies for a single game tournament.

Abstract Bracketology 1

If anyone has ideas of where to go with these, or questions to ask/answer, please comment!

...and GO DUKE!

GRE Math Quick Review: Conversions

Rounding out the subseries on fractions, decimals, and percentages, this document covers how to convert between the three forms and offers advice on how to approach problems with such conversions. Exercises, solutions, and explanations at the end, as always. You can access the document below:

GRE Math Quick Review: Conversions

For the rest of the GRE Math Quick Review Series, access the portal page.

GRE Math Quick Review: Percentages

Completing our tour of ways to represents parts, we cover percentages and their applications in today's GRE Math Quick Review Sheet. More progress towards completing our arithmetic topics. The document, as usual, can be found below:

GRE Math Quick Review: Percentages

For more topics, go to the GRE Math portal page.

GRE Math Quick Review: Decimals

Continuing in the "arithmetic" sections, the Decimals Review Sheet is live today. Coverage of the decimal concept, operations with decimals, and GRE-specific methods for dealing with decimal problems. The document can be found below:

GRE Math Quick Review: Decimals

For other GRE Math Quick Review Sheets surf over to the portal page!

GRE Math Quick Review: Fractions

Another GRE Math Quick Review Sheet is up and running today. Sticking with the "arithmetic" category, this document covers fractions and the methods you'll need to know to work with them on the GRE. The document can be found at the link below:

GRE Math Quick Review: Fractions

For more GRE Math Quick Review Sheets, take a stroll over to the portal page.

GRE Math Quick Review: Square Roots

Here is another GRE Math Quick Review. This one covers square roots (and briefly covers squaring as well), as always including a number of exercises with fully work solutions and explanations. Here's the file, and happy learning!

GRE Math Quick Review: Square Roots

For more GRE Math Quick Reviews, go to the portal page.

Sum of Prime Factors

This morning, I was reading through most recent American Mathematical Monthly journal, and read two papers; one on summing a particularly slowly converging series, the other on primality in the ring of formal power series. For some reason, this popped a problem into my head; what kind of interesting sequence can we come up with involving primes of integers?

Playing around for a bit, I decided to look at the sum of each integer's prime factors, and make a sequence from the result. After a few modifications, I came up with a couple of interesting theorems, and a few unanswered questions about the results. The work is linked below:

Sum of Prime Factors

I also wonder if similar concepts can be extended to other unique factorization domains. Let me know if you've got any ideas!

GRE Math Quick Review: Exponents

I've just posted the first in an ongoing series of GRE math review documents, this one dealing with exponents. You can access the file below, and a link has also been posted in the associated portal post.

GRE Math Quick Review: Exponents

For more GRE Math Quick Reviews, go to the portal page.

GRE Math Quick Review Series

This is another educational portal page which will house an ongoing series of documents. The documents here are intended for use when preparing for the mathematics section of the GRE (Graduate Record Exam), though they should also be useful for those studying for the SAT, SAT II (in math), or those simply wishing to review their mathematics.

Each document covers a specific mathematical topic (for example, exponents, fractions, quadrilaterals, or ratios), giving a brief overview and exposition, a list of necessary formulas, special considerations, and numerous worked examples, with solution explanations. All questions are (approximately) at the GRE level, which covers arithmetic, algebra, geometry, counting and probability, all at an undergraduate (general education) level. I hope the documents are of help to those studying out there!

Arithmetic

Exponents

Square Roots

Fractions

Decimals

Percentages

Conversions

Algebra

Geometry

Counting and Probability