The Art of Problem Solving people recently announced their new Alcumus program, which provides online lessons on assorted math topics, including probability and combinatorics, which most math textbooks do not cover well, if at all.
Update October 2011:
Alcumus currently complements our Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra textbooks, as well as our Algebra 1, Algebra 2, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra 1 online courses. We expect to continue to expand topics in Alcumus.
I am signing up all my MathCounts students. If you’re a homeschooler, we would love to have you join us!
What Is Alcumus?
Alcumus is an online program of study which interacts with the student and adapts to his or her level. As you get stronger in a topic, Alcumus automatically provides more challenging material, but if you struggle, Alcumus will give you additional practice.The current database features more than
1100 7,500 problems with fully worked-out solutions and over 60 110 video lessons — and they keep adding more.
Parents can track their students’ performance with detailed progress reports, and the students may revisit problems and lessons at any time.
How Can I Join?
According to the AoPS website, students may only sign up for Alcumus as part of a registered class. I have set up a class called “Let’s Play Math!” which is open to all interested homeschoolers and self-directed learners. Update 10/18/2011: You no longer have to join as part of a class. Just get an AoPS account and start having fun!
Problem Solving Hints
Keep scratch paper handy, and you may want a calculator for some of the more complicated problems. I’ve been relying on mental math, and I have the mistakes to show for it.
Several of the problems are challenging, because the program is trying to serve students with a very wide range of abilities. If you miss the problem, or if you click “I Give Up,” the program will show you the answer worked out. Don’t be afraid to use the “Give Up” option. If a problem is too hard for you, that means there’s a topic you can look forward to learning about.
The program always shows the solution for every problem, even the ones you get correct. If you are unsure about any of your answers, you should read the solution, even if you got the problem right. Understanding the worked-out solution may give you another way to think about the problem, or it may give you some insight that will help on a future problem.