Click to hear theme song. MAT 320: Introduction to Analysis Schedule Lectures: TuTh 10:00-11:20   SB Union 237 Recitations: MW 11:00am-11:53am   SB Union 237 Instructor Tony Phillips Office hours W 2-4   Math 3-113 TA Jonathan Hales Office hours In MLC, Weds 1:30-3:30 Mon/Weds 12:00-12:30 in SBU 239 Description A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series. Overview An introductory course in analysis, required for math majors. It provides a closer and more rigorous look at material which most students encountered on an informal level during their first two semesters of Calculus. Students learn how to write proofs. Students (especially those thinking of going to graduate school) should take this as early as possible. Prerequisites C or higher in MAT 200 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161 Textbook Kenneth Ross Elementary Analysis: The Theory of Calculus Homework Weekly problem sets will be assigned, and collected in Wednesday recitation. The emphasis of the course is on writing proofs, so please try to write legibly and explain your reasoning clearly and fully. You are encouraged to discuss the homework problems with others, but your write-up must be your own work. Late homework will never be accepted, but under documented extenuating circumstances the grade may be dropped. Grading Homework: 20%, Midterm I: 25%, Midterm II: 20%, Final: 35%.

Syllabus/schedule/homework (subject to change)
 Tue 8/28 1. Joint class: Introduction, motivation: what are real numbers? (Grushevsky) Read pages 1-15 Thu 8/30 2. Joint class: Properties of numbers; induction; concept of a field. (Grushevsky) HW due 9/5: 1.3, 1.4, 1.5, 1.12, 2.1, 2.3, 3.1, 3.5, 3.6 Tue 9/4 No class: Labor Day Thu 9/6 3. Joint class: Completeness axiom for real numbers; Archimedean principle. (Phillips) Read pages 19-25;HW due 9/12: parts ehlmno of: 4.1,4.2,4.3,4.4; and 4.8,4.10,4.11,4.12,4.15 Tue 9/11 4. Joint class: Infinity, unboundedness. Definition and examples of sequences. (Phillips) Read pages 27-41 Thu 9/13 5. Joint class: Limit of a sequence. (Phillips) HW due 9/19: 5.1, 5.2, 5.4, 7.2, 7.4, 7.5ab Tue 9/18 6. Joint class: Limit laws for sequences. (Grushevsky) Read pages 43-53 Thu 9/20 7. Joint class: Divergence to infinity, more formal proofs. (Grushevsky) HW due 9/26: 8.2ace, 8.4, 8.9, 8.10, 9.1, 9.4, 9.6, 9.9, 9.12, 9.13, 9.15 Tue 9/25 8. Joint class: Monotonic sequences, lim sup and lim inf. (Phillips) Read pages 54-63 Thu 9/27 9. Joint class: Cauchy sequences, and decimal expansion. (Phillips) No HW: prepare for the midterm Tue 10/2 Joint Midterm I in Earth&Space 131. Thu 10/4 10. Joint class: Subsequences; monotonic subsequences. (Grushevsky) HW due 10/10: 10.1, 10.2, 10.4, 10.6, 10.10, 11.2, 11.3, 11.5, 11.7, 11.10 Tue 10/9 11. § 12 Thu 10/11 12. §§ 14,15 HW due 10/17: 12.1, 12.2, 12.4, 12.8, 12.11 14.2, 14.4, 14.8, 14.9, 14.12, 14.13, 14.14 15.1, 15.2, 15.6 Tue 10/16 13. § 17 Thu 10/18 14. § 18 HW due 10/24: 17.2, 17.5, 17.6, 17.8, 17.10, 17.12a, 17.14 18.2, 18.4, 18.5, 18.6, 18.7, 18.9 Tue 10/23 15. § 19 Thu 10/25 16. § 20 HW due 10/31: 19.1bcdfg, 19.2, 19.4, 19.6, 19.7, 19.11 20.1, 20.4, 20.5, 20.8, 20.11, 20.14, 20.16, 20.17 10/29 -- 11/2 University closed: Hurricane Sandy Tue 11/06 17. § 23 Thu 11/08 18. § 24 No HW: prepare for the midterm Tue 11/13 Midterm II covers §§10, 11, 12, 14, 15, 17, 18. Thu 11/15 19. § 25 HW due Mon. 11/19: 23.1, 23.4, 23.7, 23.8, 23.9 24.1 24.2, 24.7, 24.8, 24.12 25.1, 25.2, 25.3, 25.5, 25.11 Tue 11/20 20. § 26 Thu 11/22 No class: Thanksgiving HW due 11/28: 26.2, 26.3, 26.4, 26.5, 26.6, 26.7 Tue 11/27 21. § 28 Thu 11/29 22. § 29 HW due 12/5: 28.1bc, 28.3bc, 28.6, 28.8, 28.13 29.2, 29.3, 29.5, 29.10, 29.14, 29.16 Tue 12/4 23. § 31 Thu 12/6 24. Review Final Exam: Friday, December 14, 11:15AM-1:45PM

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