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MATH 140H, Honors Calculus I – Fall 2011TERM PAPER ASSIGNMENTStephen G. SimpsonPennsylvania State UniversityNovember 9, 2011AssignmentThe 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 pageslong.• Each term paper w ill be graded as satisfactory or unsatisfactory.• A satisfactory term paper will result in a higher grade in the c ourse.DeadlinesThe deadlines are as follows.• A one-page term paper proposal or outline must be submitted electroni-cally by November 18.• The term paper itself must be submitted electronically by December 9.Suggested background readingSome 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 andAnalysis, Chels ea, 1989, XII + 418 pages.1• Elliott Mendelson, Number Systems and the Foundations of Analysis, Aca-demic Pre ss, 1973, XII + 358 pages.• Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer,1980, X + 351 pages.Suggested topicsSome suggested ter m pa per topics are as follows.• Exposition and commentary o n Sections I–VI of Dedekind’s essay “TheNature and Meaning of Numbers.”• Exposition and commentary on Sections VII–X of Dedekind’s essay “TheNature and Meaning of Numbers.”• Exposition and commentary on Sections XI–XIV of Dedekind’s essay “TheNature and Meaning of Numbers.”• Exposition and c ommentary on Dedekind’s essay “Continuity and Irra -tional Numbers.”• Peano systems: the Iter ation Theorem and its pr oof.• Peano systems: the Isomorphism Theorem and its proof.• Peano systems: definition and basic properties of addition, order, multi-plication, a nd ex ponentiation.• Peano systems: proofs of the basic pro perties of addition, order, multipli-cation, and exp onentiation.• The rational number system: constructing it from the natural numbersystem; definition of addition, order, and multiplication.• The rational number system: proofs of the basic properties of addition,order, and multiplication.• The rea l number system: Dedekind cuts.• The rea l number system: Cauchy sequences.• The real number system: proofs of the basic proper ties 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


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PSU MATH 140 - TERM PAPER ASSIGNMENT

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