Math 310, Introduction to Analysis I
Test II on Wednesday, 18 Nov, covers
sections 10, 11, 17-19: solutions
Here is a
review sheet.
Current homework:
20.14, 20.20a, 28.2a; due Fri, 20 Nov.
Read sections 28, 29
Scroll down for solutions to tests etc.
Instructor:
Alex Kumjian,
AB 619,
tel: 784-4615, e-mail: alex@unr.edu
Office Hours: MW 1:30-2:30, TR 11-11:50 or by appointment
Time and Place: MWF 11-11:50pm, AB 635
Test dates: 5 Oct, 18 Nov
Final Exam: Monday 14 Dec, 9:45 - 11:45.
Text: Elementary Analysis: The Theory of Calculus,
by Kenneth A. Ross.
Supplementary Text:
Introduction to Real Analysis,
by William Trench
Prerequisites: Math 283 or consent of the instructor.
An acquaintance with mathematical proofs
such as that provided by Math 373 is strongly recommended.
There are many good introductory books for learning the basics of
proofs, e.g. How to Prove It: A Structured Approach,
by Daniel J. Velleman or the first half of An Introduction
to Mathematical Reasoning, by Peter J. Eccles
(both books are available on
reserve). Here are some
notes
on logic and proofs that may serve as a refresher written by
my colleagues, Profs. J. Johnson and D. Pfaff. If you have
no problem doing the exercises, you should be well prepared for
the course.
See the tentative schedule.
Any changes will be announced in class.
The grader, William Taylor, has office hours TT 12-1pm, 6-7pm in AB 632.
Solutions:
Test I,
solutions.
Quiz 2 solutions.
Quiz 3 solutions.
Quiz 4 solutions.
Extra Credit: due Tue, 10 Nov.
solutions
Solutions to past homework:
1.4, 1.8a due Wed. 2 Sept,
solutions
4.1 h, j, n, p; 4.8, 4.14 a; due Fri 11 Sept,
solutions
5.2, 8.2 d, 8.4; due Fri, 18 Sept,
solutions
8.8a, 8.10, 9.1b; due Fri, 25 Sept,
solutions
10.2, 10.6a, 10.10; due Fri, 9 Oct.
solutions
11.6, 11.7, 11.10; due Fri, 16 Oct.
solutions
17.4, 17.9d, 17.10c; due Fri, 23 Oct.
solutions
18.4, 18.6, 18.10; due Mon, 2 Nov.
solutions
This is the first course of a two course sequence which lays
the foundation for the theory that makes Calculus work.
This course will emphasize the theoretical principles of Calculus
of one variable.
Most of the work will involve proofs.
Welome to Analysis! This course has two important goals: The first
is to give you a rigorous understanding of the principles
of Analysis --- this is the area of mathematics that makes Calculus
(and everything else that builds on it) work. Secondly in the process
of putting Calculus on a rigorous foundation we will need to explore
the nature of mathematical reasoning and proof. Most of the work of
this course will involve the formulation of logical written argument
rather than computation (this may take a little getting used to).
You are strongly encouraged to read the text carefully, for it is well
written and full of good examples. But it is not enough to read the
text. In order to truly master the material, you need to work with
it. Homework will therefore constitute a critical part of the
course.
The text is written by a well-known analyst and it has been a classic
text for introductory analysis for nearly thirty years (and it is still
in its first edition!). We will cover the following
sections:
| 1. |
The Set N of Natural Numbers | |
12. |
lim sup's and lim inf's |
| 2. |
The Set Q of Rational Numbers | |
17. |
Continuous Functions |
| 3. |
The Set R of Real Numbers | |
18. |
Properties of Continuous Functions |
| 4. |
The Completeness Axiom | |
19. |
Uniform Continuity |
| 5. |
The symbols +&infin and −&infin | |
20. |
Limits of Functions |
| 7. |
Limits of Sequences | |
28. |
Basic Properties of the Derivative |
| 8. |
A Discussion about Proofs | |
29. |
The Mean Value Theorem |
| 9. |
Limit Theorems for Sequences | |
32. |
The Riemann Integral |
| 10. |
Monotone Sequences and Cauchy Sequences | |
33. |
Properties of the Riemann Integral |
| 11. |
Subsequences | |
34. |
Fundamental Theorem of Calculus |
Class policy:
Attendance is encouraged but not mandatory; however you will be
responsible for everything done in class. You should also
monitor this page and your university email address for any
class announcements. Class participation is strongly encouraged!
Please ask questions.
Your basic grade will be computed with the following weights:
| Test I |
25% |
| Test II |
25% |
Homework and Quizzes |
25% |
| Final Exam |
25% |
If it helps, your final exam score may be substituted for the lowest
of the other three scores (in which case it will count 50%).
The grading scale will roughly be as follows
(plusses and minusses may be given in borderline cases):
A - 88%, B - 76%, C - 64%, D - 52%
Homework and Quizzes:
Doing mathematics is the best way of learning it especially
in a class like this -- writing proofs well only comes through
practice. Therefore homework will constitute an important part
of this class and it will be assigned regularly. All submitted
work must be written neatly in complete grammatical sentences.
You are requested to work in groups of two or three and submit
one homework assignment per group. All students in the group
will be given the same score for each assignment they collaborate on
(so each student's name must appear on each page).
One person in the group should take the responsibility of writing up
each problem in consultation with the other members of the group.
Students in a group should take turns writing up problems.
You may also talk to students in other groups to get ideas
about how to solve problems but copying is strictly forbidden.
This includes copying from any source (including phrasing from the
text or the web).
Quizzes may also be given from time to time.
As a courtesy to your fellow students please arrive on time and
make sure your cell phones are turned off during class.
No calculators or other electronic aids will be permitted during
exams.
The Math Department supports providing equal access for students with
disabilities. I encourage any student needing to request accommodations
for a specific disability to please meet with me at your earliest
convenience to ensure timely and appropriate accommodations.
return to the
Math Dept or
UNR.