**ERIC Number:**EJ944651

**Record Type:**Journal

**Publication Date:**2011-Sep

**Pages:**4

**Abstractor:**ERIC

**Reference Count:**3

**ISBN:**N/A

**ISSN:**ISSN-1947-279X

Triple Play: From De Morgan to Stirling to Euler to Maclaurin to Stirling

Kolpas, Sid

MathAMATYC Educator, v3 n1 p34-37 Sep 2011

Augustus De Morgan (1806-1871) was a significant Victorian Mathematician who made contributions to mathematics history, mathematical recreations, mathematical logic, calculus, and probability and statistics. He was an inspiring mathematics professor who influenced many of his students to join the profession. One of De Morgan's significant books was his "Essay on Probabilities and on their Application to Life Contingencies and Insurance Offices." The intent of the book was to make probability theory accessible to students who had no mathematical training beyond arithmetic. The author wondered why De Morgan's algorithm for n! worked. That led him to an intermediate algebra/college algebra investigation of the algorithm, which led to Stirling's formula, which approximates n!. Having recently taught calculus II and calculus III at his college, the author wondered why Stirling's formula so closely approximated n!. That in turn led to the Gamma Function (significantly developed by Euler), a proof by mathematical induction (De Morgan introduced the term mathematical induction, and made the process rigorous) of the Gamma Function for n! (n a whole number), and a proof of Stirling's formula using double integrals in polar coordinates, and Maclaurin series. In the process, the author also learned some mathematics history and discovered some interesting exercises for intermediate algebra, college algebra, calculus II, and calculus III.

Descriptors: Probability, Algebra, Mathematical Formulas, Logical Thinking, Mathematical Logic, Validity, Calculus, College Mathematics, History, Mathematics

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education; Postsecondary Education; Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A