**Instructor:** Harbir Antil

**Office:** Math Building 4113

**Email:** hantil@math.umd.edu

Course
Info: |
Spring 2011 |

MWF 1:00-1:50pm | |

Room 2136 (CHE Bldg) |

**Office Hours:** TBA

**Text: ***Mathematical Proofs* by Chartrand,
Polimeni and Zhang, 2^{nd} edition

**Recommended: ***Advanced Calculus* by Fitzpatrick,
2^{nd} edition, AMS (this is the text for Math 410)

**Prerequisite: **Math141

**Corequisite: **Math241.

**Course Description:** Math310 is designed to be a
lead in course to Math410 (Advanced Calculus). The goal
is to introduce you to introductory theory material and review some
calculus with proof, so
that you will be able to succeed in Math410. The majority of the course
will be spent on
introducing the theory of mathematics. You will learn different methods
of proof and how
to apply each technique to different situations. This course should not
only prepare you for
Math410, but also prepare you to study theoretical mathematics in any
area. Approximately
one third of the course will be spent reviewing some introductory
calculus material with
proof. We will discuss sequences and continuity in more detail as well.

You will be expected to read, understand and do
proofs in this course. If you are not yet comfortable with proofs you
will be by the end of the semester. To really learn mathematics you
need
to do mathematics, so you will be expected to work on problem sets. You
should also read the material from the text before each class. For a
description of the material to be covered see the math department's
course
syllabus here.
The
syllabus
I
handed
out
in
class
(in
PDF
format)
is
here.

**Rough Schedule:** We will cover Chapters 0 through 10
and 12 of Chartrand, Polimeni and
Zhang, as well as parts of Chapters 1, 2 and 3 of Fitzpatrick.

Exam 1: | Chapters 0-3 |

Exam 2: | Chapters 4-6, PHP |

Exam 3: | Chapters 7-10 |

Exam 4: | 12.1 of Chartrand and Chapters 1-2 of Fitzpatrick |

Exam 5: | Chapters 2-3 Fitzpatrick, 12.5 Chartrand |

Homework 1 is due Friday, January 28

**Grading:**

Five in-class Exams (75 pts each) | 375 pts |

Weekly Homework (20 pts each) | 220 pts |

Weekly Quizzes (15 pts each) | 180 pts |

Final (Exam | 150 pts |

Total |
925
pts |

You can find old exams given in this course at testbank.

**Honor Code:** You should be familiar with the
University's policies on Academic Integrity,
including the Honor Pledge. In this course: you are cheating on
homework if you copy someone else's work. It is fine to have someone
explain a problem to you, or show you her work; you just have to write
a solution from your own understanding, without simply copying.
Copying does not benefit you, as you are unlikely to be able to
reproduce the answer on a
quiz or exam. Homework is a very important part of this course, but
your overall understanding is more important.

**Homework Assignments:** I *encourage* you to
work in groups on the homework assignments. Homework will be assigned
daily, and collected each Friday (unless there is an exam on Friday
then homework is due Wednesday). Exam and Quiz questions will be
similar if not identical to homework questions. Quizzes will be on
Mondays (on the homework due the previous Friday) and days before exams
(on all material since the last exam). I expect to assign somewhere
between 6 and 12 problems each day, but I will only collect 6 problems
at a time. I will not specify in advance which problems will be
collected. For this reason each problem must be done on a separate page
(or partial page) and you must include your name on each page (or
partial page). Late homework will not be accepted, except in extreme
cases. All odd numbered questions have answers/solutions in the back,
therefore I will not collect odd problems (except in rare situations.)
However, I will assign them and expect that you understand them for
quizzes and exams. So, you should only look at the solutions if you are
really stuck and try to only look as far into the solution as you need.

I reserve the right to give unannounced quizzes and make changes in the
syllabus
that I feel are necessary. Any changes in the syllabus will be
announced in class and posted to the website.

Assignment |
Assigned Problems |
Due Date |

Assignment 1 | 1.1, 1.2, 1.4, 1.7, 1.11, 1.18, 1.19, 1.22, 1.24, 1.41, 1.51, 1.52, 2.1, 2.2, 2.3, 2.4, 2.8 | 1/28/11 |

Assignment 2 | 2.10, 2.11, 2.14, 2.16, 2.19, 2.20, 2.22, 2.24, 2.28, 2.31, 2.32, 2.33, 2.34, 2.37, 2.39, 2.40, 2.45, 2.46, 2.48 (a-f), 2.51, 2.57, 2.61, 2.62, 3.1, 3.3 | 2/4/11 |

Assignment 3 | 3.6, 3.7, 3.11, 3.12, 3.14, 3.17, 3.18, 3.20, 3.22, 3.23, 3.27, 3.29, 3.32, 3.33, 3.38, 3.43 | 2/11/11 |

Assignment 4 | 4.3, 4.4, 4.5, 4.18, 4.19, 4.20, 4.25, 4.49, 4.50, 4.54, 4.55, 4.62, 4.66, 4.68 | 2/18/11 |

Assignment 5 | 5.2, 5.4, 5.11, 5.12, 5.13, 5.14, 5.16, 5.21, 5.22, 5.28, | 2/25/11 |

Assignment 6 | 5.32, 5.33, 5.35, 5.36, 5.43, 5.45, 5.46, 6.2, 6.4(1), 6.15, 6.19, 6.21, 6.32, 6.35, 6.38, 6.43, 6.48 | 03/04/11 |

Assignment 7 | 7.7, 7.8, 7.16, 7.20, 7.23, 7.27, 7.32, 7.38, 7.39, 7.41, 7.42, 7.49, 7.57, 7.65, 7.71, 7.72 | 03/14/11 |

Assignment 8 | 8.3, 8.4, 8.5, 8.9, 8.12, 8.15, 8.16, 8.46 | 03/18/11 |

Assignment 9 | 9.3, 9.4, 9.6, 9.11, 9.13, 9.17, 9.21, 9.25, 9.26, 9.30, 9.37, 9.43, 9.46, 9.48, 9.52 | 04/1/11 |

Assignment 10 | F: 1.1 #2, 11, 13, 14,; 1.2 #1, 3, 5, 6, 7; 1.3 #8, 14, 15 | 04/13/11 |

Assignment 11 | HW 11 | 04/22/11 |