Instructor: Maksim Maydanskiy, maksimm@math.stanford.edu
Office: 382E. Office hours: Tuesday 2:15-3:45, Friday 2:15-3:45 or by appointment.
Course Assistant: Beniada Shabani, bshabani@math.stanford.edu
Office: 380-L Office hours: Monday 2:05-4:05, Tuesday 1:05-2:05.
Grades should be entered in the next couple of days. Thank you and have a nice winter break.
Dec 14: Final and solutions to final are posted.
Dec 12: Solutions to practice final are posted.
Dec 11: HW8 returned. Please pick up from my mailbox.
Practice final is posted.
Extra office hours Wednesday and Thursday 2:15-3:45 and by appointment.
Dec 4: Final review will take place in Herrin 195T (same place as the lectures). It's still on Friday, Dec 7th starting at 4:30 pm.
Dec 4: Lectures 27 and 28 posted. Solutions to HW8 posted.
Dec 3: Final review will take place on Friday, Dec 7th starting at 4:30 pm (roughly 1.5 hrs, but will depend on interest.) Location TBD.
Comments
Preliminary Course Outline
Homework and notes will appear here.
Note on mindmaps: Mind maps are graphical representations of information. I will also post basic mindmaps of lectures created using FreeMind, both in the native .mm format and exported as pdf. I encourage you to use these to create more prsonaliszed versions as a study strategy and a review tool. If you have questions about mind maps let me know.
| Week 1 | Sep 24 - Sep 28: | Introduction. Induction. Rational numbers. | |||
| Mind maps: Natural Numbers and Induction: mm, html(flash), pdf; Rational Numbers: mm, html(flash), pdf | Lecture 1, Lecture 2, Lecture 3 | Supplementary notes on natural number system. | |||
| Week 2 | Oct 1 - Oct 5: | Real numbers. | HW 1 due. | ||
| Mind maps: Real numbers: mm, html(flash), pdf | Lecture 4, Lecture 5, Lecture 6 | Answers to question and concerns 1 | HW1 Solutions, comments. | ||
| Week 3 | Oct 8 - Oct 12: | Sequences. | HW 2 due. | ||
| Mind maps: Limit of a sequence: mm, html(flash), pdf | Lecture 7, Lecture 8, Lecture 9 | Supplementary notes on proof creation and proof writing. | HW2 Solutions, comments. | ||
| Week 4 | Oct 15 - Oct 19: | Sequences. | HW 3 due. | ||
| Lecture 10, Lecture 11, Lecture 12 | Answers to question and concerns 3 | HW3 Solutions, comments. | |||
| Week 5 | Oct 22 - Oct 26: | Sequences. Midterm review. | Practice midterm, solutions. | ||
| Mind maps: Real Analysis Part I: mm, html(flash), pdf | Lecture 13 | Midterm, solutions | |||
| Midterm exam on Friday, Oct 26. | |||||
| Week 6 | Oct 29 - Nov 2: | Sequences (end). | HW 4 due. | ||
| Lecture 14, Lecture 15, Lecture 16 | HW4 Solutions, comments. | ||||
| Week 7 | Nov 5 - Nov 9: | Series. | HW 5 due. | ||
| Lecture 17, Lecture 18, Lecture 19 | HW5 Solutions, comments. | ||||
| Week 8 | Nov 12 - Nov 16: | Continouous functions. | HW 6 due. | ||
| Lecture 20, Lecture 21, Lecture 22 | HW6 Solutions | ||||
| Thanksgiving break. | |||||
| Week 9 | Nov 26 - Nov 30: | Uniform continuity and limits of functions. | HW 7 due. | ||
| Lecture 23, Lecture 24, Lecture 25 | Supplementary notes on lower semi-continuity and proof of uniform continuity. | HW7 Solutions | |||
| Week 10 | Dec 3 - Dec 7: | Sequences and series of functions. | HW 8 due. | ||
| Mind maps: Review mm, html(flash), pdf | Lecture 26, Lecture 27, Lecture 28 | HW8 Solutions | |||
| Final exam 12/14/2012 8:30-11:30 AM in Herrin 195T | Practice final, Solutions, Final, Solutions | ||||
Grade Policy
Lowest 2 homework scores will be dropped. Homework 20 %, Midterm 30%, Final 50%.
Course Objectives
The goal of this course is to understand the theory behind single variable calculus. This includes understanding real numbers, their sequences and series, limits, continuous functions, derivatives and integrals. Honors math majors and students who intend to do graduate work in mathematics should take 171.
Homework
Homework is due weekly in Wednesday lecture, as detailed in the course outline. Late homework will not be accepted, absent a bona fide emergency; however the lowest 2 homework scores will be dropped. You are encouraged to discuss homework with me, your CA, and your classmates, however the final write-up should be entirely your own. We abide by the Honor Code.
Extra Help
Dot not hesitate to come to my office during office hours or by appointment to discuss a homework problem or any aspect of the course. You also may want to consider talking to Stanford University Mathematical Association(SUMO).
Important dates
Textbook
We will follow Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross.
Similar material is covered in the first part of Undergraduate Analysis, by Serge Lang, which you may consult if you want to see a different exposition.
Prerequisites
Old Announcements
Dec 3: Lecture 26 posted.
Nov 30: Lecture 25 posted.
Nov 29: HW8 posted. HW7 solutions are posted. Lecture 24 posted.
Nov 26/2: Supplement 3 posted.
Nov 26: Lecture 23 posted.
Nov 16: Lectures 21 and 22 posted. HW7 posted. HW 6 solutions posted. Grader comments for HW5 posted. Happy Thanksgiving!
Nov 12: Lectures 19 and 20 posted.
Nov 7: HW5 solutions posted. HW6 posted. Lecture 18 posted.
Nov 5: Grader comments for HW 4 posted. Lecture 17 posted.
Nov 2: HW 5 corrected. Lecture 16 posted.
Nov 1: HW4 Solutions posted.
Oct 31: HW5 posted. Lecture 15 posted.
Oct 29: Lecture 14 posted.
Oct 26: The midterm and solutions to midterm posted. HW 4 updated (2 more problem added). Oct 25: The Solutions to Practice Midterm posted.
Oct 23: Mindmap of "Real Anlysis Part I" posted. Even if you have ignored the mindmaps till now, this may be the time to give them a try. Make your own or expand this one (say, by adding HW problem numbers to the nodes).
Oct 22. Lecture 13 posted. Office hours this week moved from Friday to Thursday, 2:15-3:45. Let me know if you would like to come to office hours on Thursday but can't make the time specified.
Oct 21: Practice Midterm and grader comments on HW 3 posted.
Oct 19: Homework 3 solutions posted.
Final exam time and location announced: December 14, 8:30-11:30 am, in HerrinT195, same room as the lectures.
Vi Hart gives 9.999... reasons why 0.999...=1, and then why they are all wrong (note the upload date).
She also explains the difficult relation Pythagoras had with irrationality and beans, a subject we touched upon in Lecture 2.
Oct 17: The midterm location is confirmed - 380-380W. This is in the basement of the math building. Midterm time is 10-11:30 and 4-5:30 on Friday Oct 26.
First part of homework 4 is up. Homework 4 is due in about 2 weeks- Wednesday, October 31. However if you want to get a leg up and practice the latest material before the midterm you can start on it.
Lecture 11 notes up.
Questions and Concerns for week 3 are up.
Oct 12: The supplementary notes on proof creation and proof writing are posted. I strongly encourage you to take a look and read the parts that seem relevant for you.
Midterm is preliminarily scheduled for Friday 10-11:30 with alternate time of 4-5:30 that evening. If you can not make both of those times let me know by Monday end of lecture. Midterm location is to be determined.
Lecture 8 notes updated, Lecture 9 notes up.
Oct 8: Courtsework site is live, and grades for HW1 posted. Survey results are here and also here: The first two bar charts are difficulty/speed of lectures and length/difficulty of homework. Most people answered "3-Just about right". The other three charts are overall impression of the course, understanding of material and important vs. unimportant concepts in the course.