**Course Information**- Week 1: Metric spaces, convergence of sequences, open and closed sets, relatively open and closed sets
- Week 2: Cauchy sequences, complete metric spaces, compact sets, Heine-Borel theorem, continuity, connected sets.
- Week 3: Pointwise and uniform convergence of sequences and series of functions. Uniform convergence, continuity, and integration; Weierstrass M-test.
- Weeks 4/5: Uniform convergence and derivatives; Weierstrass approximation theorem; power series; exponential and log functions; trig functions.
- Week 6: Periodic functions, trigonometric polynomials, trigonometric Weierstrass approximation theorem, Fourier series, Plancherel theorem
- Week 7: Review of linear transformations, differentiation in several variable calculus, Clairaut's theorem, chain rule, inverse function theorem, implicit function theorem
- Weeks 8/9: Outer measure; measurable sets; Lebesgue measure; measurable functions; simple functions
- Week 10: The Lebesgue integral; monotone convergence theorem, Fatou's lemma, and dominated convergence theorem; comparison with Riemann integral; Fubini's theorem
- A supplemental handout on logic. You may also enjoy these lighter-hearted logic puzzles of Lewis Carroll as practice.
- A supplemental handout on set theory.
- Real analysis was developed by several key mathematicians,
mostly in the nineteenth century, including Cantor,Cauchy,Dedekind,Hilbert,Lebesgue,Peano,Riemann,
and Weierstrass;
these links point to biographies of these famous mathematicians.

Official stuff | Stuff specific to 131BH/1 Spring 2003 |

(*) - The course description and textbook and schedule are for 131B, not 131BH, so these pages are only a very rough guide as to what to expect from the course.

We recommend that you read the lecture
notes and the textbook
concurrently with (or prior to) the lectures. If you only read these
sources occasionally and after the fact (e.g. when your homework is due)
then you will not get the most out of the course.

We will be assuming familiarity with the material in 131AH; some lecture notes on that material can be found here for reference.

We will be assuming familiarity with the material in 131AH; some lecture notes on that material can be found here for reference.