### 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?**

And speaking of fun, that’s what we had last summer at the first camp. Nine math enthusiasts flew into town for the four day event. For a taste of what it was like, this article from the Albuquerque Journal delivers!

**A powerful, inspiring review of the first MathCamp4Adults:**

“As a secondary mathematics instructor, I want my students to participate in specific disciplinary practice and to understand how practices relate to broader realms of the mathematical community of ideas. With so much of mathematics instruction focused on tools for manipulating equations, students grow eager to engage with mathematics on a verbal and more conceptual level. At Math Camp, I encountered both some of the big concepts that have shaped mathematical exploration for centuries and even millennia. Math Camp offered a terrific survey of fundamental problems and solutions, and through Kaylee’s measured yet efficient stewardship, my fellow campers and I navigated an extremely broad range of ideas in a way that was both accessible and challenging.

Like many math teachers, I believe that thinking mathematically is a natural human process, and that most minds are drawn to mathematical questions. From early experiences drawing arrows on the ends of number lines, big questions about continuity, infinity, and even cardinality follow students as they progress from year to year. One of the most satisfying aspects of Math Camp for me was the clear road map from these deeper questions back to familiar tools of secondary mathematics, and the unexpected relationships that the deeper questions bring to light. I especially appreciated the care given to the scheduled progression through topics, as it allowed us to build upon ideas and to circle back and tie them in in new ways. One would be hard pressed to find another program that builds a bridge from primes to transcendental numbers in three days, all in the company of fellow math fans with expert support. All through Math Camp runs a current of enthusiasm and curiosity that is always refreshing to those working to broaden the community of ideas that we love.”

Thomas Priestley, Educator

** Comments on the evaluation forms for the first camp:**

“Kaylee (the instructor/facilitator) was great — very knowledgeable and enthusiastic. I really enjoyed the camp and look forward to the next camp.”

“Kaylee was excellent in every way. He managed to keep it fun and showed great fluency with a huge range of topics. This was a great experience. I loved being able to “play” in this environment.”

“I appreciated Kaylee’s excitement and passion for the topics. The group dinner was fun!”

“Excellent! I would attend another camp. Topics can be repeated, no problem. The philosophical implications are the most interesting to me.”

“Awesome topics! Great review after being away from math for too long. Kaylee was great with leading discussions, presenting material, explaining, and encouraging exploration. With the success of this first session, the next should bring more interest and participants.”

**Average score from all participants for “Overall value of the camp”: 4.85 out of 5.**

### 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:

–Pythagorean Theorem

–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 will use the difference of squares method to design an algorithm that can find every possible triple. Then we’ll try to come up with formulas that generate triples.

** Fermat’s Last Theorem **Related to the concept of Pythagorean Triples, Pierre de Fermat, in the 17th century, posited that:

Simple enough for a child to understand, and with no counter examples ever found, proof eluded mathematicians for over 300 years.

** 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.

** Liar’s Bingo**

** 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

Register **here**.

**Adjunct Faculty for the Breckenridge camp:**

**Dr. William Dunham will be presenting and assisting alongside the MathCamp4Adults team. **

Bill is a professor at Muhlenberg College and the author of numerous books on mathematics, including our favorite:

We are honored to welcome Bill Dunham to MathCamp4Adults!

For a more detailed bio of Bill and the rest of our staff, click here.

To ask a question or submit content ideas:

#### Our favorite math quote of all time, and one which you will be able to explain after attending MathCamp4Adults:

“The algebraic numbers are spotted over the plane like stars against a black sky; the dense blackness is the firmament of the transcendentals.” — Eric Temple Bell

**All after-tax profits from tuition are donated to scholarship programs for math students and to programs that provide training for math teachers. **

**MathCamp4Adults PO Box 15912**

**Rio Rancho, NM 87174-5912**

**Tel: 1-505-331-4303**

Andy.Klee@MathCamp4Adults.com