Mathpage

We have used a fairly standardized approach toward mathematics at an accelerated pace. We started with the Exploring Mathematics K-8 texts (1994) from Scott Foresman along with the Sets and Numbers books by Patrick Suppes from the 1960's. I believe that these are still available from Stanford.

For our son, we did first, second, third and fifth grade and then went straight to Algebra I. We are currently working on Calculus using Salas and Hille, Geometry (Jacobs), Discrete Mathematics (Rosen) and competition-style problem solving using Mathcounts.

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• Elementary Algebra, Harold Jacobs, (BC QA152.2.J33). We used this with our son and it was very enjoyable. A nice review of his books is available at Math Textbooks by Harold Jacobs. A shorter review is available at the Holt Bookstore.
• Intermediate Algebra, Lial & Miller. I looked at about a dozen books and found this to be the best text for this subject. It isn't in typical high-school text reviews as it is considered a college text. We used this to finish up Algebra II after doing most of it using a text that we borrowed from the local district.

• Calculus, Salas and Hille. Calculus through multivariable. A proof-oriented text that I used in college. It's quite a bit of work to slog through the limit proofs in chapter two but after that, it's not that bad.
• Calculus, Tom Apostol. Very highly regarded older text. We gave it a try for calculus I but it was too difficult.
• Foundations of analysis. Landau. A nice little book for middle-school students. Answers the question: what is a number?
• How to solve it. Polya. Recommended on misc.education.
• Precalculus by Lial. A modern text though I think that this is out of print now. Their new version uses much more of a graphing approach. We used this text with our son and liked it.
• Calculus links
  • AP-CALC archive at The Math Forum. Discussions on teaching AP math topics.
  • A brief history of calculus. It is very brief though references are provided for more detail.
  • Common Errors in Undergraduate Mathematics site by Eric Schechter at Vanderbilt. This page is useful for for students to read from time to time to develop good habits in working through problems.
  • e-Calculus from the University of Akron (Department of Mathematics and Computer Science. They have a set of pdf documents that can be used as slides to aide with learning calculus. I looked at one of the pdf files and what I saw looked good.
  • Karl's Calculus Tutor. He has a bunch of tutorials that currently covers limits and derivatives and it looks like he has more to add. He also answers questions via email. And his site has a great links page.
  • Visual Calculus site, recommend on the AP-Calculus mailing list. The site has tutorials and demonstrations though I haven't done any exploring here yet. The site is at the University of Tennessee and I had some problems getting to it.
• QuizStar site. It contains links to lectures and quizzes in College Algebra, Statistics, Trigonometry and other math and some non-math topics.

• Calculation Tips from The Math Forum. They have hundreds of mental calculation tips, divisibility rules and multiplication tips.
• Exploring Mathematics (K-8), 1994, Scott Foresman. I liked the series though you have to know what you're doing as it isn't always obvious from the text. It's an NCTMish text with lots of color, multicultural stuff, and calculator usage. It is quite generous with problem sets.
• Sets and Numbers (1-6), 1960s, Patrick Suppes. An old New Math series. Used in Stanford's EPGY program. I believe that you can get photocopies or CD-ROMs from Stanford. This is a good program though it may be useful to supplement the material with newer materials and more exercises.

• American Mathematics Society. Purpose is to further mathematical research and scholarship.
• Mathematically Correct, an anti-new-new-math group. They also provide curricular reviews.
• Mathematics Association of America. They are devoted to the interests of collegiate mathematics.
• Project 2061, a project of the American Association for the Advancement of Science has textbook ratings for Algebra and Middle Schools.
• Society of Actuaries. These are the guys that figure out how long you're going to live.

• The American Mathematics Competitions site. Contains information on the competitions, has an order form for previous tests, the schedule of exams and associated events along with exam descriptions. The exams look fairly inexpensive and are copyright with no duplication permitted. They also explicitly include home school students as being elegible for their competitions.
• Annual High School Mathematics Examinations (AHSME) various years, C. T. Salkind.
• From Erdos to Kiev: problems of Olympiad caliber, Ross Honsberger, MAA, 1996. BC QA43.H65 1996.
• Highline Advanced Math Program is an enrichment program for grades 5 through 7. The site contains sample fifth- and sixth-grade problem sets.
• Hungarian Problem Book I, J.Kurchak, 1963, 0-88385-611-5.
• International Mathematical Olympiad site contains problems from past competitions and links to country sites. Note that some of the tests are in TEX or DVI form.
• International Mathematical Olympiads, 78-85, Klamkin, BC ERC QA43.K46.
• International Mathematical Olympiads, 59-78, Greitzer, BU Sci QA43.G7.
• The Mandlebrot Competition contains some sample problems at the middle-school level. They also have packets that you can purchase.
• Math and Computer Competitions. Pointers to competition sites.
• Math League Multimedia contains information on math league competitions and they sell products. They have sample test questions for different levels.
• MathCounts. This is a program to encourage students to pursue math at the middle-school level. They provide quite a few problem sets of interesting problems.
• Mathematical gems from ..., Honsberger, BC QA164.H78 1973.
• The Third International Mathematics and Science Study (TIMMS), site contains released items for math and science at the elementary, middle-school and high-school level. Tests, results and analysis are available at this site.
• U.S.A. mathematical olympiads, 72-86, Klamkin.
• The USSR olympiad problem book, BU Sci QA43 F62.
• The USSR Olympiad Problem Book : Selected Problems and Theorems of Elementary Mathematics, by N.D. Chentzov, I.M. Yaglom, Irving Sussman (Editor), D. O. Shklarsky, 1993, BC QA 43.55823.

• Agnesi to Zeno : over 100 vignettes from the history of math, Sanderson Smith, Key Curriculum Press, 1996. A middle-school-level math history teacher's text suitable for independent reading. Also has activities. BC ERC QA 21.S658 1996.
• Classic Math: History Topics for the Classroom , by Art Johnson, Dale Seymour Publications, 1994. A classroom-oriented book for teachers to provide interesting topics for classes. Contains a Quote of the Week section which has short biographies and a quote. Also contains Event of the Week, Historical Problems, History of Mathematical Symbols, History of Mathematical Terms and Solutions and Extensions.
• History (Clark University Links).
• An Introduction to the History of Mathematics, Howard Eves, 1976, Holt, Rinehart and Winston. Recommended on the home-ed mailing list. Not reviewed yet.
• Mathematical People: Profiles and Interviews, Albers and Alexander. Quite an interesting book with mathematicians from the 1900s. More diagrams than your typical history book. I think that this book may be good for reading to your kids.
• Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Luetta Reimer and Wilbert Reimer, Dale Seymour Publications, 1990, 0-86651-509-7. ERC QA28.R44. A nice collection of stories about mathematicians suitable for reading to elementary-age children. Covers Thales, Pythagoras, Archimedes, Hypatia, Napier, Galileo, Pascal, Newton, Euler, Lagrange, Germain, Gauss, Galois, Noether and Ramanujan.
• Mathematics: From the Birth of Numbers, by Jan Gullberg, WW Norton. Said to be a complete history of numbers. It's on my list to perhaps use for math.
• Modern Mathematicians by Harry Anderson. Enjoyable for middle- or high-school students. Mathematicians: Babbage, Lovelace, Boole, Cantor, Kovalevskaia, Noether, Ramanujan, Ulam, Chern, Turing, Robinson, Mandelbrot and Conway. 1996 by Facts on File, Inc.
• What is Mathematics, Richard Courant and Herbert Robbins, Oxford, 1941. Recommended on the home-ed mailing list. I haven't reviewed this yet.

• Factasia logic site. Contains descriptions of the various types of logic to a good amount of detail.
• Home School Logic Course, something I'm working on for Fall 2000.
• Introduction to Logic by Irving Copi. The standard university text. Covers reasoning as well as formal logic.
• Introduction to Logic, Suppes, BC BC108.S85, BU BC108.F571. A good first-year introduction to logic.
• A Logical Approach to Discrete Math by David Gries and Fred Schneider. Very nice logic-based discrete math text with a good treatment on logic itself.
• Mathematical Logic For The Schools, Suppes. Aimed at fifth-graders though it is out of print. Covers proposition and predicate calculus.

• aha! Gotcha: Paradoxes to Puzzle and Delight by Martin Gardner. Another book popular with home schoolers. Useful to illustrates paradoxes and conundrums at a level that children can understand.
• aha! Insight by Martin Gardner. A book popular with home schoolers on problem solving. It contains cartoons to help with understanding the problem along with insight as to how to do the problem. Usable with children.
• The Art and Craft of Problem Solving by Paul Zeitz. This book is aimed at the high-schooler with very good math preparation for those interested in high-school math contests. It could also be used for a one-semester college course on problem solving. It assumes a little familiarity with calculus.
• The Art of Problem Solving, Volumes 1 and 2 and their solution manuals by Lehoczky and Rusczyk. These are geared for high-school competitions. They review high-school math material and cover a few things that you generally only see on competition problems. You can order these at the Mu Alpha Theta site.
• Brain Teasers from Houghton Mifflin contains word problems every week.
• Creative puzzles of the world, Pieter van Delft, Key Curriculum Press, 1995. BC ERC GV1493.D4 1995.
• Five Hundred Mathematical Challenges, Edward Barbeau, Murray Klamkin, William Moser, MAA, 1995. BC ERC QA43.B37 1995.
• Get it together : math problems for groups, grades 4-12, Tim Erikson, EQUALS, Lawrence Hall of Science (Berkeley), 1989. BC ERC QB43.E64 1989.
• Interactive Mathematics Miscellany and Puzzles site. Contains puzzles and Java-based math games along with fun and interesting facts about math and answers to certain common math questions. (added March 10, 1997)
• INTERNET MATH CHALLENGE at the University of Idaho. They have a weekly drawing of correct answers for a tee-shirt. But they have a nice selection of problems to download and look at.
• Japanese Math Challenge. Contains 20 story problems translated from Japan's Jr. High Math Tests. Also has an ad for a CD-ROM for more problems.
• Math Proficiency Test for ninth grade.
• MathStories.com, contains word problems for grades 1-5.
• Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, George Polya, 1981, in two volumes. I had a quick look at this in the library and it looks quite useful. BC QA43.P62.
• NRICH Maths - the Online Maths Club
• Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures, Michael Serra, Key Curriculum Press, 1994. BC ERC QA63.H37 1994. A very nice textbook, suitable for a semester or two on problem-solving that can get kids and adults to think in different ways.
• Puzzles and Problems, a page with links to sites with math puzzles and problems.
• Stand up math : 180 fun and challenging problems for kids!, James Riley, GoodYearBooks, 1995. BC ERC QA11.R55 1995.
• Think-ercises : [math & word puzzles to exercise your brain], Terry Stickels, Critical Thinking Press & Software, c1995. BC ERC GV1493.S75 1995.
• University of Central Florida CASIO CONTEST PAGE
• Word Problems for Kids at St. Francis Xavier University, contains lots of word problems for fifth-graders through twelfth-graders.

• CRC Handbook of Math Tables (Chemical Rubber Company). I picked up my first copy in my early teens and marvelled over areas of mathematics that I hadn't been exposed to. I quite enjoyed the formulas to produce beautiful polar graphs.
• Eric Weisstein's World of Mathematics, an encyclopedia of mathematics which is quite good.

• Math and Reason, Dr. Alan Selby. He has a guide to math and logic.
• The Math Forum, loads and loads of math resources and chat areas.
• Mathematics Archives at the University of Tennessee, Knoxville. I haven't reviewed this but it looks promising.
• Sheila King's links. A math teacher with lots of good links at her site.

• GNUPlot - graphings software. Many recent math textbooks assume that you have graphing calculators available so that students can whip up plots without the drudgery of calculating and plotting points. I like to see the basic skill mastered first, but after this, I've found that GNUPlot (find it on YAHOO and download it) is nice and easy to use for our current Algebra II course.
• Java-based slide rule.
• Peanut Software is a site at Phillips Exeter Academy in Exeter, NH. Their site contains a number of Windows and DOS programs to add in the teaching of mathematics. The programs were recommended on a bulletin board though I haven't tried them out yet.
• Webmath.com. This site contains calculators, equation solvers, converters, plotters that are web-based and free. They also sell a PC version of their software. The neat thing about the tools on this site is that some of the tools explain what they do in english before giving you the answer. This might be quite useful for a child.