Mathematics 250 - Number Theory and Mathematical Reasoning

Institution:

Colgate University

Subject:

Description:

E. Hart, D. Saracino, T. Tucker, K. Valente Questions about the positive integers 1, 2, 3 . . . have fascinated people for thousands of years. The ancient Greeks noted the existence of right triangles with sides of integral length, corresponding to equations such as 32 + 42 = 52 and 52 + 122 = 132. Is there a way of describing all such "Pythagorean Triples" As another example, we observe that 5 = 12 + 22, 13 = 22 + 32, 17 = 12 + 42, while none of the primes 7, 11, or 19 can be expressed as the sum of two squares. Is there a pattern Does it continue forever This course focuses on such equations as a means for introducing students to the spirit and methods of modern mathematics. The emphasis throughout is on developing the ability to construct logically sound mathematical arguments and communicate these arguments in writing. Prerequisite : MATH 11 2 o r 11 3 with a grade of C or better, or permission of the instructor.

Credits:

1.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Multiple

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.colgate.edu

Phone Number:

(315) 228-1000

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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