Math 310 - Introduction to Analysis

Instructor: Dr. Kathryn Truman
Office: Math Building 1113
Email: rendke (at math dot umd dot edu)

Course Info: Spring 2008
TuTh, 12:30 - 1:45
Room 1308 (Math Bldg)

Office Hours: TBA.

Text: Mathematical Thinking, D'Angelo

Grader: TBA


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 series in more detail as well. We will also spend time gaining a deeper understanding of the real numbers as a field.

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 departments course syllabus here. The syllabus I handed out in class (in PDF format) is here.


Chapters and sections to be covered (tentative):
Exam 1Chapters 1 and 2
Exam 2Chapters 3, 4 , 7, 10, and 12
Exam 3Chapters 13, 14, and possibly 15
FinalCumulative - so all material covered

Quizzes and Exams:
Exam 1
Exam 2
Exam 3
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7
Quiz 8
Quiz2, part 1
Quiz 7, two
Group Quiz 2


Grading:
Three 1.25 hour Exams (100 pts each)           300 pts
Daily Homework 180 pts
Weekly Quizzes 120 pts
Final (Cumulative) 150 pts
Total 750 pts


Exam/Quiz Makeup Policy: Exam/Quiz makeups will only be given for University Excused Absences. Any student with a valid reason to be excused from an exam must contact me prior to the exam, either by email or by phone (leave a message at 301.405.5047), and present documentation at the next class session attended. If you need to be excused for a religious observance, you should let me know as soon as possible, but in any case no later than the end of the schedule adjustment period.

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: Homework will be assigned and due daily. I expect to assign somewhere between 6 and 12 problems each day, but I will only collect 3 problems the next class period. I will not specify in advance which problems will be collected. For this reason each problem must be done on a separate page and you must include your name on each page. Late homework will not be accepted, except in extreme cases. Quiz and exam problems will be similar to assigned homework problems. The text has hints to many problems. To learn best, you should not look at the hints unless you are really stuck. I reserve the right to give unannounced quizzes and make changes in the syllabus that I feel are necessary. These changes will be announced in class and posted to the website. It is advisable to keep up with class work and attend class regularly. Extra help is available during my office hours and by appointment. All assignments are tentative until given in class - you are responsible for checking this page or asking me for updates if you miss class.

Homework Assignments
AssignmentAssigned Problems
Assignment 1: Due January 31 1.1, 1.5, 1.6, 1.7, 1.9, 1.10, 1.13
Assignment 2: Due February 51.14, 1.18, 1.21, 1.24, 1.25, 1.32, 1.38, 1.41
Assignment 3: Due February 71.42, 1.45(a,c), 1.47, 1.49, 1.55(extra)
Assignment 4: Due February 122.1, 2.2, 2.4(a,b,d), 2.9, 2.21, 2.24, 2.32
Assignment 5: Due February 142.10(a-d), 2.23, 2.25, 2.26, 2.29(a), 2.37
Assignment 6: Due February 192.38, 2.42, 2.44, 2.45, 2.47, 2.49, 2.50(a), 2.51
Assignment 7: Due February 212.12, 2.13, 2.16, 2.34, 2.36, 2.52
Assignment 8: Due March 4 3.2, 3.3, 3.5, 3.8, 3.10, 3.15, 3.17, 3.22, 3.28, 3.35
Assignment 9: Due March 6 3.41, 3.45, 3.49, 3.55, 3.56
Assignment 10: Due March 11 12.1, 12.2 (For 12.2 the forumla is a_n = 2 * (-1)^(n+1) + 3 * 2^n) You need to prove both these formulas by induction! 12.19, 12.21, 12.31
Assignment 11: Due March 13 4.4, 4.7, 4.11, 4.12, 4.22
Assignment 12: Due March 25 4.9, 4.10, 4.27, 4.31, 4.33, 4.34, 4.35
Assignment 13: Due March 27 4.42, 4.43, 4.44, 4.46, 4.47
Assignment 14: Due April 1 7.10, 7.11, 7.12, 10.2, 10.4, 10.14, 10.18
Assignment 15: Due April 15 13.4, 13.8, 13.9, 13.19, 13.22, 13.24
Assignment 16: Due April 17 13.10, 13.11, 13.20, 13.23, 13.25, 13.26
Assignment 17: Due April 22 13.19, 13.27, 13.29, 13.34 + Handout given out in class.
Assignment 18: Due April 24 13.30, 14.8, 14.11, 14.14, 14.15, 14.21
Assignment 19: Due April 29 14.1, 14.2, 14.3, 14.9, 14.18, 14.19, 14.25
Assignment 20: Due May 1 14.5, 14.10, 14.13, 14.33, 14.49, 14.50
Assignment 21: Due May 6 14.27, 14.43, 14.45, 14.46 + quiz corrections