- Instructor: Mikhail Ershov
- Office: Kerchoff 302
- e-mail: ershov
*at*virginia*dot*edu - Office hours: Tue 3:30-4:30, Wed 2:15-3:15 (Clark 101), Wed 4:45-5:45 by APPOINTMENT
- Course webpage:
*http://people.virginia.edu/~mve2x/3310_Spring2015*

A note on proofs. MATH 3310 is a proof-based course. Everything we discuss in class will be rigorously proved. More importantly, you are expected not only to understand proofs, but also to learn how to construct your own proofs and how to write proofs (so that others can understand your argument). It is not expected that you have taken a proof-based course before MATH 3310. However, MATH 3310 will not include any lectures devoted specifically to proof writing; instead you will be expected to develop this skill gradually as we progress through the material. If you feel that you need a more detailed introduction to proof writing, I encourage you to take MATH 3000 (Transition to Higher Mathematics) before or concurrently with MATH 3310. MATH 3000 is offered this semester and will meet MWF 10-10:50am.

week | sections | topics |

Jan 13, 15 | 1.1, 1.2 | Introduction. Ordered field axioms. |

Jan 20, 22 | 1.3 | Least upper bounds. Completeness axioms. |

Jan 27, 29 | 2.1, 2.2 | Limits of sequences. Limit theorems. |

Feb 3, 5 | 2.3, 2.4 | Bolzano-Weierstrass Theorem. Cauchy sequences |

Feb 10, 12 | 1.6, 3.1 | Countable and uncountable sets. Limits of functions. |

Feb 17, 19 |
3.2, First midterm. | One-sided limits. Limits at infinity. |

Feb 24, 26 | 3.3 | Continuity. |

Mar 3, 5 | 3.4, 4.1 | Uniform continuity. The derivative. |

Mar 17, 19 | 4.2, 4.3 | Differentiability Theorems. Mean Value Theorem. |

Mar 24, 26 | 4.4 | Taylor's Theorem and L'Hospital's Rule. |

Mar 31, Apr 2 | 4.5, Second midterm. | Inverse function theorems. |

Apr 7, 9 | 5.1, 5.2 | The Riemann integral. Riemann sums. |

Apr 14, 16 | 5.2, 5.3 |
More on Riemann sums. The Fundamental Theorem of Calculus. |

Apr 21, 23 | 6.1, 6.2 |
Introduction to series. Series with non-negative terms. |

Apr 30 | 6.3 | Absolute convergence. |

- homework: 15%
- midterms: 20% each
- final: 45%

- First midterm exam: Thu, Feb 19th
- Second midterm exam: Thu, Apr 2nd
- Final exam: Mon, May 4th, 9am-12pm

- Make-ups will be given only under extreme circumstances (such as serious illness). Except for emergencies, you must obtain my permission for a make-up before the exam.
- If you miss an in-class exam or fail to submit a take-home exam
by the due date without a compelling reason, you will
be assigned the score of
**0**on that exam. - University regulations specifically prohibit early make-ups.

- Homework will be assigned weekly and will usually be due on Thursday.
- Please STAPLE your homework.
- No late homework will be accepted. However, three lowest homework scores will be dropped.
- GRADING: it will not be possible to grade all homework problems. In each assignment 3-4 selected (but not announced in advance) problems will be graded for credit.

- You are welcome (and even encouraged)
to work on homework together, but you
*must*write up solutions independently, in your own words. In particular, you**should not be consulting others during the process of writing down your solution**.

- Monday, January 26 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
- Tuesday, January 27 -- Last day to DROP a course (deletion from the transcript)
- Wednesday, March 18 -- Last day to withdraw from a course