# The Pennies For Proofs scholarship is currently discontinued.

The University of Alaska Fairbanks Department of Mathematics and Statistics is pleased to offer the 2013 Pennies for Proofs scholarship program.

### 2013 Fall Competition

The Department of Mathematics and Statistics is offering \$500 tuition credits for freshmen or sophomores enrolling in Math 215 (Introduction to Mathematical Proofs) in Spring 2014. Students from all majors are welcome to apply.

To be eligible to apply for this scholarship, you must

• Have freshman or sophomore standing; preference will be given to first-year students.
• Have at least a 3.0 average in all mathematics courses taken an UAF.
• Agree to take Math 215 in Spring 2014 if you accept an award.

Scholarships will be awarded based on review of a completed application, which consists of:

1. A completed Pennies for Proofs Application Form.
2. A statement of interest: in no more than 250 words discuss what you find appealing about mathematics.
3. A completed Pennies for Proofs Recommendation Form. This form must be completed by a current mathematics instructor.

Application deadline: November 30, 2013

#### About Mathematics and Proof

Mathematics has two great traditions: computation and proof. Most of your mathematics studies have been devoted to learning computation skills. Calculus is, for example, one of the finest computation tools we have. If you decide to pursue any of a number of science or engineering degrees at UAF, Calculus II is a required class and you will want to take it early in your studies.

Proofs are different. The goal of a proof is not to arrive at a number, but to show that a mathematical fact is true. For example, the early Egyptians had a rule of thumb that a triangle with side-lengths 3, 4, and 5 has a right angle. By contrast, the early Greeks had a proof that the triangles with right angles are exactly the triangles where the side lengths satisfy a2 + b2 = c2 (Euclid, Book I, Propositions 47 and 48).
Here are some things you can show using proofs:
• At any given time, there are two exactly opposite points on the Earth where it is exactly the same temperature.
• It is impossible to comb the hairs on a sphere so that all the hairs lie flat.
• Fundamental Theorem of Algebra: every polynomial equation has at least one complex solution. Maybe someone mentioned this to you in an algebra class. Is it true? How would you know?
In Math 215, Introduction to Mathematical Proofs, you learn the skills needed to put a proof together and to analyze someone else's proof. These are the skills you need to have before tackling any of results mentioned above. By learning about this side of mathematics, you'll gain a better understanding of all your mathematics courses.