Math 312 : Concepts of Real Analysis
PROFESSOR: ||Dr. Jenny X. Li|
Office: 220 McAllist Building
office hours: Tue. 11:30-12:30, Friday 11:30-12:30 or by appointment
COURSE:|| An introduction to rigorous mathematical proofs which
involving properties of real numbers, sequences, continuity, series of
function, differentiation and integration.
TEXTBOOK:|| Elementary Analysis: The Theory of Calculus
by Kenneth A. Ross 2th edition., Springer
REFERENCE:||Introduction to Analysis by Arthur Mattuck, latest edition
PREREQUISITES:|| Math 141
- Homework and Quizzes (25%): Every week.
- Midterm (35%): Oct.15 at regular lecture time.
- Final Exam (40%): Time and place will be announced.
- NO late homework will be accepted, but the lowest grade of homework will be dropped. Also there will be NO makeup midterm.
- Quizzes will occur whenever it is necessary. They will be announced in advance, also No makeup quizzes.
- Bonus questions will be given throughout the semester which will be added to the final grade.
- NO books, notes, calculators or other electronic devices are permitted in the quizzes, midterm or final exam.
- PART I Introduction
- The sets of Naturally and Rational Numbers
- The set of Real Numbers
- The Completeness Axiom
- PART II Sequences
- Limits of Sequence
- Monotone Sequences and Cauchy Sequences
- Lim sup's and lim inf's
- Alternating Series and Integral Tests
- PART III Continuity
- Continuous Functions
- Properties of Continuous Functions
- Uniform Continuity
- Limits of Functions
- Topological Concepts in Metric Spaces
- More on Metric Space: Continuity and Connectedness
- PART IV Sequences and Series of Functions
- Uniform Convergence
- Differentiation and Integration of Power Series
- Weierstrass's Approximation Theorem
- PART V Differentiation
- Basic Properties of the Derivative
- The Mean Value Theorem
- L'Hospital's Rule
- Taylor's Theorem