Math 4130 Honors Introduction to Analysis I Spring 2009 General information Your instructor is Victor Protsak MT 432 and can be reached at 255 4373 or protsak at math cornell edu The class meets TR 8 40 9 55 am in MLT 207 Your TA is Mihai Bailesteanu MLT 120 mbailesteanu at math cornell edu Homework and the course announcements including possible changes to the syllabus will be posted at the course webpage http www math cornell edu protsak hia html Catalogue description Prerequisite high level of performance in MATH 2210 2220 2230 2240 or 1920 and 2940 and familiarity with proofs Introduction to the rigorous theory underlying calculus covering the real number system and functions of one variable Based entirely on proofs The student is expected to know how to read and to some extent construct proofs before taking this course Topics typically include construction of the real number system properties of the real number system continuous functions differential and integral calculus of functions of one variable sequences and series of functions Scope We will cover chapters 1 7 of the textbook Robert Strichartz The Way of Analysis revised edition Jones and Bartlett 2000 ISBN 0 7637 1497 6 A good complementary source for exercises is the book Walter Rudin Principles of mathematical analysis 3rd edition McGraw Hill 1976 Homework There will be a weekly homework assignment due on Thursday before 3 pm in my office you can also turn it in at the lecture Late homework may be accepted only in exceptional circumstances at the discretion of the instructor Make sure that you have studied the textbook and understood both the theory and what is required of you on any given assignment before starting to work on it To earn the full credit your reasoning must be correct and your presentation clear Your paper must be neatly written or typed and stapled Course work It is in your best interest to thoroughly study the book and solve as many problems as you can Anticipated time commitment 8 to 12 hours a week outside of class Remarks on proofs One of the challenges in this course involves translating between intuitive thoughts often expressed in ordinary language and formal mathematical statements that may involve special terminology and mathematical notation You will spend much of your time learning analyzing constructing and writing down rigorous proofs of various mathematical statements When you read a statement or analyze its proof you need to recognize the meaning behind the formal logic and symbols on the other hand when you solve a problem or prove a statement yourself you will have to express your ideas in a rigorous way You should practice writing out proofs from the textbook and the lecture and then compare your version with the original they do not have to be identical but you must correctly reproduce the same steps and present them in good style Exams and grading There will be two prelims and a final exam Your course grade will be weighted as follows Homework 40 Prelims 30 Final 30 Academic integrity You are encouraged to discuss theory and problems from the course with your classmates However copying other people s work is not allowed You should be familiar with and must abide by the Code of Academic Integrity Help and feedback I urge you to approach me and your TA if anything is unclear Questions that affect a sizeable part of the class will be discussed in the lecture I will welcome your feedback about my teaching and any concerns that you might have about this course