MATH 140H Honors Calculus I Fall 2011 TERM PAPER ASSIGNMENT Stephen G Simpson Pennsylvania State University November 9 2011 Assignment The assignment is as follows Each student in this course is required to submit a term paper The topic of the term paper is to be selected by the student The topic should be on some aspect of the foundations of calculus The term paper should be neatly typewritten and at least 5 to 10 pages long Each term paper will be graded as satisfactory or unsatisfactory A satisfactory term paper will result in a higher grade in the course Deadlines The deadlines are as follows A one page term paper proposal or outline must be submitted electronically by November 18 The term paper itself must be submitted electronically by December 9 Suggested background reading Some references on the foundations of calculus are as follows Richard Dedekind Essays on the Theory of Numbers Dover 1963 III 115 pages Solomon Feferman The Number Systems Foundations of Algebra and Analysis Chelsea 1989 XII 418 pages 1 Elliott Mendelson Number Systems and the Foundations of Analysis Academic Press 1973 XII 358 pages Kenneth A Ross Elementary Analysis The Theory of Calculus Springer 1980 X 351 pages Suggested topics Some suggested term paper topics are as follows Exposition and commentary on Sections I VI of Dedekind s essay The Nature and Meaning of Numbers Exposition and commentary on Sections VII X of Dedekind s essay The Nature and Meaning of Numbers Exposition and commentary on Sections XI XIV of Dedekind s essay The Nature and Meaning of Numbers Exposition and commentary on Dedekind s essay Continuity and Irrational Numbers Peano systems the Iteration Theorem and its proof Peano systems the Isomorphism Theorem and its proof Peano systems definition and basic properties of addition order multiplication and exponentiation Peano systems proofs of the basic properties of addition order multiplication and exponentiation The rational number system constructing it from the natural number system definition of addition order and multiplication The rational number system proofs of the basic properties of addition order and multiplication The real number system Dedekind cuts The real number system Cauchy sequences The real number system proofs of the basic properties of addition order and multiplication Proof of the Heine Borel Theorem Continuous functions rigorous definition and basic properties Continuous functions proof of the Extreme Value Theorem Continuous functions proof of the existence of the Riemann integral Continuous functions proof of the Fundamental Theorem of Calculus 2