Overview This is an introductory course to proof-based mathematics. We will be interested in understanding the rigorous foundations of single variable calculus, in particular, properties of the real numbers, limits, continuity, differentiation, and the Riemann integral.
Office My office is 744 in the Mathematical Sciences building.
Office hours M 3:30-4:30; T 5:30-6:30; F 11:30-12:30; or by appointment.
Text The required textbook for this class is Introduction to Analysis by Arthur Mattuck.
A copy of the textbook is available from Amazon's CreateSpace publishing for $15. Here is a link to purchase.
Academic Calendar For ease of reference, here is a link to the academic calendar detailing all breaks, add/drop deadlines, etc.
Accommodations In this mathematics course accommodations are managed between the instructor, student, and the DRC Testing Center. You should make a brief appointment with me to discuss your accommodations as soon as possible. Purdue University strives to make learning experiences as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, you are welcome to let me know so that we can discuss options. You are also encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247.
Exams There will be four exams, the first three in class and the last during the final exam period. (See below for schedule and further details.) One exam will be dropped. Please contact me as soon as possible when you become aware of any exam conflicts or if you have missed an exam.
Alternate Examination Alternately, you may obtain credit on any or all exams by oral examination. Intent to take such an exam must be communicated at least 3 business days prior to the scheduled exam date. Exam scores obtained by oral examination are final and are not subject to dispute.
Homework There will be weekly homework sets. (See below for details and due dates.) Students are encouraged to collaborate on homeworks as long as: 1) all collaborators are listed on the cover sheet of each student's assignment; 2) each student turns in their own, individual work. Rote copying of solutions from peers, internet forums, or plagiarism of any kind will not be tolerated.
Homework Formatting Homeworks must be typed or neatly written on loose leaf paper (no fringes!). There should be no significant cross-outs, rewrites, scratchwork, scribbling, etc. Problems should be clearly indicated and pages must be securely fastened together. Homework should have a cover sheet attached with your name, course section (either 31 or 52), the homework set number, and the names of your collaborators, in that order.
Late Homework Late homework will only be accepted if turned in to me in person during office hours. As part of the conditions of acceptance, you may be asked to present your solution of a problem of my choosing. No penalty will be assessed for assignments which are not excessively late (less than one week past due).
Quizzes There will be several quizzes throughout the semester. Quizzes will be announced at least one class period in advance. At least one quiz will be dropped, maybe more depending on the total number of quizzes.
Grades After drops, each item in a given category receives equal weighting. Your percentage of points earned in each category will be combined into a single score with weighting 63% on exams, 32% on homeworks, and 5% on quizzes. Grades will be assigned based on rank among all students in both sections. For marginal cases, there will be some discretionary leeway in final grade assignment to account for course participation/engagement or extraordinary effort. The following is a sample cutoff distribution which is fairly typical for courses I have previously taught. The final grade cut-offs may differ slightly. A >92, A- >88, B+ >84, B >77, B- >73, C+>69, C> 64, C- >60.
Academic Integrity See the Academic Integrity webpage from the Office of the Dean of Students. Penalties for academic dishonesty will be, at minimum, a score of zero on the exam or assignment. Egregious cases will be referred to the Dean of Students and may result in failure of the course or expulsion.
LaTeX is the language for mathematical typesetting. If you are a CS, Math, or Stats major, I would strongly recommend becoming proficient in LaTeX. Here is the link to A.J. Hildebrand's excellent collection of beginner LaTeX resources. Another great place to start is Jon Peterson's advice and resources for new researchers. You will probably also frequently need to consult the LaTeX Wiki.
Mental Health If you find yourself beginning to feel some stress, anxiety and/or feeling slightly overwhelmed, try WellTrack. Sign in and find information and tools at your fingertips, available to you at any time.
If you need support and information about options and resources, please see the Office of the Dean of Students for drop-in hours (M-F, 8 am- 5 pm). If you’re struggling and need mental health services: Purdue University is committed to advancing the mental health and well-being of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of mental health support, services are available. For help, such individuals should contact Counseling and Psychological Services (CAPS) at (765)494-6995 during and after hours, on weekends and holidays, or by going to the CAPS office of the second floor of the Purdue University Student Health Center (PUSH) during business hours.
The following is a tentative outline of topics covered and is subject to change. If you are absent from class it is your responsibility to find out what material was covered and to obtain notes from classmates.
Week 1 Basic Set Theory, Logic, and Proof Techniques (Appendices A, B)
Week 2 Real Numbers, Monotone Sequences (1); Estimations (2); Definition of a Limit (3.1, 3.2)
Week 3 MLK DAY; Limits (3.3-3.7); Error Terms (4)
Week 4 Limit Theorems (5); Completeness (6)
Week 5 Infinite Series (7); LEEWAY/REVIEW; EXAM 1
Week 6 Powers Series (8); Functions of One Variable (9), Local and Global Principles (10)
Week 7 Continuity (11); Intermediate Value Theorem (12)
Week 8 Continuous Functions on Compact Intervals (13), Differentiation (14)
Week 9 LEEWAY/REVIEW; EXAM 2; Differentiation (14)
Week 10 SPRING BREAK
Week 11 Differentiation (15); Linearization (16); Taylor Series (17);
Week 12 Integrability (18); The Riemann Integral (19);
Week 13 The Riemann Integral (19); Derivatives and Integrals (20);
Week 14 LEEWAY/REVIEW; EXAM 3; Sequences of Functions (22);
Week 15 The Lebesgue Integral (23); Continuous Functions on the Plane (24)
Week 16 LEEWAY/REVIEW
Assignment 1, Due: Wednesday, January 16 Graded problems. In addition, review Questions A.1.1, A.2.1, A.3.1 (answers are in the book), but do not submit.
Assignment 2, Due: Wednesday, January 23 Graded problems.
Assignment 3, Due: Wednesday, January 30 Graded problems.
Assignment 4, Due: Wednesday, February 13 Graded problems.
Assignment 5, Due: Wednesday, February 20 Graded problems.
Assignment 6, Due: Wednesday, February 27 Graded problems.
Assignment 7, Due: Friday, March 8 Graded problems.
Assignment 8, Due: Wednesday, March 27 Graded problems.
Assignment 9, Due: Wednesday, April 3 Graded problems.
Assignment 10, Due: Wednesday, April 24.
Quiz 1, 1/18. Solution.
Quiz 2, 1/28. Solution.
Quiz 3, 2/15. Solution.
Quiz 4, 2/22. Solution.
Quiz 5, 3/25. Solution.
Quiz 6, 4/3. Solution.
Quiz 7, 4/17.
Friday, February 8 A, B, Chapters 1-6, and related homeworks and lectures.
Key.
There will be an extra office hour in REC 316, Wednesday, 2/6, 4:30-5:30.
Wednesday, March 6 Chapters 7-13 and related homeworks and lectures.
Key.
Wednesday, April 10, Chapters 14-19 and related homeworks and quizzes.
Key.
Monday, April 29 Chapters 20, 22-24 and related homeworks and lectures.