Class: MTuWTh 2:00P-3:59P | 242 Hearst Gym
Instructor: Ved V. Datar
Email: vv lastname at math.berkeley.edu, no spaces
Office: 1067 Evans Hall
Office hours: MTuW 4PM-5:00PM
Text: Kenneth Ross, Elementary Analysis, (any edition)
Suplementary reading: Stephen Abbott, Understanding analysis.
Homeworks - 15%, Midterm - 35%, Final - 50%
There will be 7 homeworks, of which 6 will be graded, and only the best five will be counted towards the grade. Late submissions of homeworks will not be graded.
There will be one midterm and one final exam, each of 100 points. There will be no make-up exams. In the end, the final exam score (appropriateley scaled) can replace the midterm score. But note that final, being cummulative, is expected to be more challenging than the midterm, so you are advised to not skip the midterm. To pass the class, you have to take the final exam.
If you are a disabled student (with or without a document from the Disabled Students' Program) and require special accommodations of any kind, please e-mail the instructor as soon as possible, and no later than June 30th.
If you are representing the university on some official duties (say if you are an athlete or in a band), and if there is a conflict with any of the mid-terms, please let the instructor know before January 30th.
You can find important deadlines on adding and dropping courses here.
To do well in the course, it is important to be able to understand as well as write proofs. It might be useful to read Prof. Hutching's article on mathematical reasoning.
Most of our proofs will use standard set theoretc notation. Here are some notes from Prof. Bergman on set theory.
We will also often use mathematical induction. Here are some notes on that by Prof. Bergman.
Some additional warm up problems (not to be submitted) to get comfortable with basic set theory and induction, and their solutions (not to be looked at until you have tried all the problems).The page numbers refer to Ross' book.
| Number | Date | Topic | Reading | Homework | Notes |
| 1 | M 06/18 | introduction, number systems, definition of reals | 1-13 | A1 (due 06/25) Solutions | Week-1 |
| 2 | Tu 06/19 | real numbers (cont.), consequences of completeness axiom | 13-29 | ||
| 3 | W 06/20 | sequences, some standard limits, properties | 33-55 | ||
| 4 | Th 06/21 | monotone sequences, limsup and liminf | 56-66 | ||
| 5 | M 06/25 | subsequential limits, Bolzano-Weierstrass, Cauchy criteria | 66-82 | A2 (due 07/02) Solutions | Week-2 |
| 6 | Tu 06/26 | infinte series, limsup-liminf, ratio/root tests | 95-109 | ||
| 7 | W 06/27 | infinite series (cont.), catch-up | 95-109 | ||
| 8 | Th 06/28 | continuity, basic properties, | 123-133 | ||
| 9 | M 07/02 | uniform continuity | 139-153 | A3 (due 07/09) Solutions | Week-3 |
| 10 | Tu 07/03 | extremum and intermediate value theorem | 133-140 | ||
| W 07/04 | holiday | 56-58 | |||
| 11 | Th 07/05 | functional limits, discontinuities | 153-164 | ||
| 12 | M 07/09 | differentiation, chain rule e | 223-232 | A4 (not graded) Solutions | Week-4 |
| 13 | Tu 07/10 | mean value theorems, L'Hospital's rule | 232-249 | ||
| 14 | W 07/11 | Taylor's theorem, catch-up | 249-268 | ||
| 15 | Th 07/12 | Riemann-Darboux integration | 269-280 | ||
| M 07/16 | Midterm and Solutions | 70-72 | A5 (due 07/23) Solutions | ||
| 16 | Tu 07/17 | Criteria for integrability, integrability and continuity | 272-291 | Week-5 | |
| 17 | W 07/18 | properties of integrals, application to infinite series | 272-291, 107-109 | ||
| 18 | Th 07/19 | Fundamental theorem of calculus and consequences | 291-298 | ||
| 19 | M 07/23 | sequences of functions, uniform convergence | 193-200 | A6 (due 07/30) Solutions | Week-6 |
| 20 | M 07/24 | uniform convergence and continuity, differentiation and integration | 200-208 | ||
| 21 | W 07/25 | power series | 187-192 | ||
| 22 | Th 07/26 | power series (cont.), elementary functions | 208-216 | ||
| 23 | M 07/30 | equicontinuity, Arzela-Ascoli | A7 (due 08/06) Solutions | Week-7 | |
| 24 | Tu 07/31 | Arzela-Ascoli (cont.), metric spaces | 110-111 | ||
| 25 | W 08/01 | open/closed sets, continuity | 83-95 | ||
| 26 | Th 08/02 | compact sets | 83-95 | ||
| 27 | M 08/06 | completeness | 128-132 | Completeness | |
| 28 | Tu 08/07 | Review | 164-178 | ||
| W 08/08 | Review | Practice Problems and Solutions | |||
| Th 08/09 | Final Exam |