Born out of a passion for mathematics. Aimed at the adult enthusiast.
MathCamp4Adults will expand your knowledge of and appreciation for math.
If you enjoy working with some of the classics of mathematics, think that ‘recreational mathematics’ is not an oxymoron, and want to ‘do math’ in a supportive environment with other math fans—then this is the summer vacation for you!
After all, why should the kids have all the fun?
Wide Variety of Topics
The Green Dot Problem. We’ll stretch your logical thinking skills with this challenging group activity.
Mathematical Proofs. We’ll develop proofs for each of the following topics:
–Square Root of 2 is Irrational, and can we also prove that unless an integer is a perfect square, its square root is also irrational?
–“Exact” square roots of integers cannot have anything to the right of the decimal point.
–Any angle inscribed in a semicircle is always a right angle
–The area of a circle
–Goldbach’s Conjecture — every even number >2 is the sum of two primes
–There exists no largest prime number, i.e., there are infinitely many primes
Infinite Series…Divergerent, Convergent? Telescoping?
Squaring the Rectangle…Triangle…Lune. And can the circle be squared? We’ll start by showing you how to construct a rectangle whose area matches the square. Then you’ll be challenged to do one (or both) of the other two constructions.
The 10 Envelopes Problem — show us what you can do with $1000 and 10 envelopes. (Sorry, the money is like -1^(1/2) — imaginary!
Fractions from 1/2 to 1/20 Believe it or not, there’s a lot of learning to be gained by calculating and discussing the decimal equivalents of a few fractions. We’ll team up to avoid some of the drudgery, but prepare to be amazed!
The Candy Monster Problem Everyone can come up with their own strategy—then we’ll discuss and look at the math behind it.
Probability — we’ll cover a few interesting problems, including:
What is the probability that from a deck with 100 numbers, from 1 to 100, you would randomly pick an odd number greater than 50?
What is the probability that two random numbers are coprime–i.e., they share no common factors other than 1. The answer actually involves Pi!
Pythagorean Triples Everyone knows that 3-4-5 is the basic Pythagorean Triple—3 squared plus 4 squared equals 5 squared. We’ll look at formulas that generate more Triples, and then use the difference of squares method to try to design an algorithm that can find every possible Triple.
Fermat’s Last Theorem Related to the concept of Pythagorean Triples, Pierre de Fermat, in 17XX, posited that there are no whole numbers such that:
Phi We will define Phi and derive its value using algebra. We’ll also discover and prove the relationship between the Fibonacci sequence and Phi. And we’ll also take a dive into the Phi-nary number system.
Games and the People that Play Them We’ll play some games, discover winning strategies and discuss the mathematics behind game theory.
Calculus, Infinite Series, and the Transcendance of Pi and e
–Crash course in Calculus—a few basics to set the stage.
–Maclaurin Series (Taylor Series)
–“Miracle” Formula: ( e^(i*theta) = cos(theta) + i*sin(theta). Also known as Euler’s Formula: e^(i π) + 1= 0
–How can these five basic concepts be related? How can it be applied—for example what are the three cube roots of -64?
Cantor, Cardinality, and the Uncountable Infinity of the Real Numbers Despite the countable infinity of the algebraic numbers (rational and irrational numbers) — the real numbers are uncountably infinite. What “accounts” for this fact?
The math camp you’ve been waiting for, even if you didn’t know it!
Join us Summer, 2018 in Breckenridge, Colorado or Albuquerque, New Mexico.
Tuition: $495 USD
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