Mathematics (MATH) 
202 Fenton, 5413464705
College of Arts & Sciences



Course Data
MATH 307 Introduction to Proof >4 
4.00 cr. 
Proof is how mathematics establishes truth and communicates ideas. Introduces students to proof in the context of interesting mathematical problems. 
Grading Options: 
Optional; see degree guide or catalog for degree requirements

Instructor: 
Polishchuk A 
Office:
207 University Hall
Phone:
(541) 3465635

Prereqs/Comments: 
Prereq: MATH 247 or 252 or 262. 



CRN 
Avail 
Max 
Time 
Day 
Location 
Instructor 
Notes 

13990 
2 
24 
12001250 
mtwf 
222 LA 
Polishchuk A 
! 
Final Exam: 
10151215 
r 12/09 
222 LA 

Academic Deadlines
Deadline 
Last day to: 
September 26: 
Process a complete drop (100% refund, no W recorded) 
October 2: 
Drop this course (100% refund, no W recorded; after this date, W's are recorded) 
October 2: 
Process a complete drop (90% refund, no W recorded; after this date, W's are recorded) 
October 3: 
Process a complete withdrawal (90% refund, W recorded) 
October 3: 
Withdraw from this course (100% refund, W recorded) 
October 4: 
Add this course 
October 6: 
Last day to change to or from audit 
October 10: 
Process a complete withdrawal (75% refund, W recorded) 
October 10: 
Withdraw from this course (75% refund, W recorded) 
October 17: 
Process a complete withdrawal (50% refund, W recorded) 
October 17: 
Withdraw from this course (50% refund, W recorded) 
October 24: 
Process a complete withdrawal (25% refund, W recorded) 
October 24: 
Withdraw from this course (25% refund, W recorded) 
November 14: 
Withdraw from this course (0% refund, W recorded) 
November 14: 
Change grading option for this course 
 You can't drop your last class using the "Add/Drop" menu in DuckWeb. Go to the “Completely Withdraw from Term/University” link to begin the complete withdrawal process. If you need assistance with a complete drop or a complete withdrawal, please contact the Office of Academic Advising, 101 Oregon Hall, 5413463211 (8 a.m. to 5 p.m., Monday through Friday). If you are attempting to completely withdraw after business hours, and have difficulty, please contact the Office of Academic Advising the next business day. 


Expanded Course Description
The discipline of mathematics includes two related strands: calculation (the main avenue of application of mathematics) and proof (the means by which mathematical truth is verified, and by which calculational algorithms are shown to be correct). Most of our math courses through the 200level are devoted to calculation (and to applications of calculation). By contrast, this course is devoted to teaching techniques of mathematical proof and formalism in the context they naturally arise for working mathematicians: while trying to understand interesting problems.
By teaching students about how to do and think about proof, this course introduces students to the foundation of mathematics as a discipline (and thus is a science group satisfying course). For math majors (or minors) this course can also serve as a bridge between the calculation and application based courses that most students take at the 100 and 200level in mathematics and the more theoretical content of many 300 and 400level courses.
This course will address fundamental questions such as
"What is a proof and how are basic proofs constructed?"
"What is mathematical induction, and what different kinds of proofs are there?"
"How does one understand and use logical constructions such as converse and contrapositive?"
"What does it mean to prove some fact which is already familiar and believable?"
"How does one start with an interesting problem, work through examples to form a strategy for a proof capturing the essence of the problem?"
The specific mathematical topics used to address these questions include:
the meaning (to a mathematician) of equations and sets,
the relationship between set theoretic and logical properties (for example between inclusion of sets and logical implication),
using induction in a wide array of settings (including establishing equalities and inequalities and analyzing "games"),
counting basic structures such as subsets and permutations,
basic properties of numbers (such as unique factorization of integers into primes, or ability to divide with remainder),
Fermat's Little Theorem and its usage in cryptography,
the analysis of graphs and associated structures (orientations and colorings) and how they can be used to model problems.



