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Fall 2021

 

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Mathematics (MATH)
202 Fenton, 541-346-4705
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
See CRN for CommentsPrereqs/Comments: Prereq: MATH 247 or 252 or 262.
 
  CRN Avail Max Time Day Location Instructor Notes
  13989 0 0 0800-0850 mtwf 119 FEN tba !

Final Exam:

1015-1215 t 12/07 119 FEN
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
Caution 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, 541-346-3211 (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 200-level 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 200-level in mathematics and the more theoretical content of many 300- and 400-level 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.

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