Introduction to Real Analysis I - Math 311 - Section 04
Lecturer: Vladimir Scheffer. Office: Hill 246. Office Hours: MTh 11:40am to 1:00pm. Email address: scheffer@math.rutgers.edu
Meeting Times: Monday and Wednesday 1:40pm to 3:00pm in Tillett 252 on LIvingston Campus. Thursday 1:40pm to 3:00pm in SEC 204 on Busch Campus.
Textbook: Introduction to Analysis by Edward D. Gaughan, 5th edition. We will cover chapters 1 through 4, and some of Chapter 0.
Topics to be Covered: Epsilon-N definition of convergence. Arithmetic operations on convergent sequences. Least upper bound and greatest lower bound principles. The Archimedean property. Monotone sequences. Cauchy sequences. Limits of functions. The algebra of limits of functions. Limits of monotone functions. Continuity at a point. Continuity on a set. Uniform continuity. Open sets, closed sets and compact sets. Differentiation. The algebra of differentiation. Rolle's Theorem. The Mean Value Theorem. L'Hospital's Rule. The Inverse Function Theorem.
Grading scheme for Math 311, section 04: The final exam will be worth 200 points. Each of the two hourly exams will be worth 100 points. The workshop writeups will be worth 60 points. The homework from the textbook will be worth 40 points. This way, the maximum course score is 500 points. Your course grade will be determined by this score.
The exams: The exams are closed book. No notes are allowed. Calculators are not allowed. The internet is not allowed. You will have to write correct proofs. If you miss an exam, then you must get a written excuse from your dean before you can take a makeup exam.
Course Learning Goals: The primary goal is to acquire the ability to write rigorous proofs of elementary real analysis theorems. Very often, these proofs will use epsilon/delta arguments. Another goal is to learn the statements and proofs of some of the fundamental theorems of real analysis, such as the Bolzano-Weierstrass Theorem. Another goal is to learn some of the fundamental concepts of real analysis, such as the notion of compactness.
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