Math 4130, Honors Introduction to Analysis ISpring 2009General information Your instructor is Victor Protsak, MT 432, andcan be reached at 255-4373 or protsak “at” math.cornell.edu. The classmeets TR, 8:40–9:55 am, in MLT 207. Your TA is Mihai Bailesteanu, MLT120, mbailesteanu “at” math.cornell.edu. Homework and the course an-nouncements, including possible changes to the syllabus, will be posted atthe course webpagehttp://www.math.cornell.edu/˜protsak/hia.htmlCatalogue description Prerequisite: high level of performance in MATH2210–2220, 2230–2240, or 1920 and 2940 and familiarity with proofs.Introduction to the rigorous theory underlying calculus, covering the realnumber sys tem and functions of one variable. Based entirely on proofs. Thestudent is expected to know how to read and, to some extent, constructproofs before taking this course. Topics typically include construction ofthe real number system, properties of the real number system, continuousfunctions, differential and integral calculus of functions of one variable, se-quences and series of functions.Scope We will cover chapters 1–7 of the textbookRobert Strichartz, The Way of Analysis (revised e dition), Jones and Bartlett,2000 (ISBN: 0-7637-1497-6)A good complementary source for exercises is the bookWalter Rudin, Principles of mathematical analysis, 3rd edition, McGrawHill, 1976Homework There will be a weekly homework ass ignment due on Thurs-day before 3 pm in my office (you can also turn it in at the lecture). Latehomework m ay be accepted only in exceptional circumstances at the discre-tion of the instructor. Make sure that you have studied the textbook andunderstood both the theory and what is required of you on any given assign-ment beforestarting to work on it! To earn the full credit, your reasoningmust be correct and your presentation clear. Your paper must be neatlywritten or typed and stapled.Course work It is in your best interest to thoroughly study the book andsolve as many problems as you can. Anticipated time commitment: 8 to 12hours a week outside of class.Remarks on proofs One of the challenges in this course involves trans-lating between intuitive thoughts, often expressed in ordinary language, andformal mathematical statements that may involve special terminology andmathematical notation. You will spend much of your time learning, analyz-ing, constructing, and writing down rigorous proofs of various mathematicalstatements. When you read a statement or analyze its proof, you need torecognize the meaning behind the formal logic and symbols; on the otherhand, when you solve a problem or prove a statement yourself, you willhave to express your ideas in a rigorous way. You should practice writingout proofs from the textbook and the lecture and then compare your versionwith the original: they do not have to be identical, but you must correctlyreproduce the same steps and present them in good style.Exams and grading There will be two prelims and a final exam. Yourcourse grade will be weighted as follows:• Homework 40%• Prelims 30%• Final 30%Academic integrity You are encouraged to discuss theory and problemsfrom the course with your classmates. However, copying other people’s workis not allowed. You should be familiar with and must abide by the Code ofAcademic Integrity.Help and feedback I urge you to approach me and your TA if anythingis unclear! Questions that affe ct a sizeable part of the class will be discussedin the lecture. I will welcome your feedback about my teaching and anyconcerns that you might have about this