Introduction to Analysis I

310 INTRODUCTION TO ANALYSIS I (3+0) 3 credits

An examination of the theory of calculus of functions of one-variable with emphasis on rigorously proving theorems about real numbers, convergence, continuity, differentiation and integration. Prereq(s): MATH 283.

Mathematics 310 is the first course in the UNR mathematics curriculum where the emphasis is on mathematical proof and reasoning. This course focuses on a rigorous justification of the topics covered in Mathematics 181-283 and provides a stepping stone to higher-level mathematics. There will be homework assignments and quizzes weekly. Mathematical proofs should be carefully written using complete English sentences, proper grammar, spelling and punctuation. This is a hard course.

Fall 2007

Course Information

Instructor:

Eric Olson

email:

ejolson at unr edu

Office:

MWF 12am Ansari Business Building AB 614 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/310/

Text:

Frank Dangello, Michael Syfried, Introductory Real Analysis, 2000, Houghton Mifflin Company.

Supplementary Text:

Robert C. Wrede, Murray Spiegel, Schaum's Outline of Advanced Calculus, Second Edition, McGraw-Hill.

Section:

001 Math 310 Introduction To Analysis I

MWF 11:00-11:50am AB 205

Grading

    10 Quizzes                      10 points each (drop 2)
    10 Homework Assignments         10 points each (drop 2)
    2 Exams                        100 points each
    1 Final Exam                   140 points
    -------------------------------------------------------
                                   500 points total

Calendar

#   Date     Chapter     Topic
------------------------------------------------------------------------
1   Aug 27    1.1        Proofs
2   Aug 29    1.2        Sets
3   Aug 31    1.3        Functions
    Sep 3                Holiday (Labor Day)
4   Sep 5     1.4        Mathematical Induction
    Sep 6                Final date for withdrawing with refund
5   Sep 7     2.1        Algebraic and Order Properties of R
6   Sep 10    2.2        The Completeness Axiom
7   Sep 12    2.3        The Rational Numbers are Dense in R
8   Sep 14    2.4        Cardinality
9   Sep 17    3.1        Convergence
10  Sep 19    3.2        Limit Theorems
11  Sep 21    3.2        Limit Theorems continued...
12  Sep 24    3.3        Subsequences 
13  Sep 26    3.3        Subsequences continued...
14  Sep 38    3.4        Monotone Sequences 
15  Oct 1     3.4        Monotone Sequences continued...
16  Oct 3     3.5        Bolzano-Weierstrass Theorems
17  Oct 5                Review
18  Oct 8                Exam I
19  Oct 10    3.5        Bolzano-Weierstrass Theorems continued...
20  Oct 12    3.6        Cauchy Sequences
21  Oct 15    3.6        Cauchy Sequences continued...
22  Oct 17    3.7        Limits at Infinity
23  Oct 19    3.8        Limit Superior and Limit Inferior
                         Final date for dropping class no refund
24  Oct 22    4.1        Continuous Functions
25  Oct 24    4.2        Limit Theorems
    Oct 26               Holiday (Nevada Day)
26  Oct 29    4.2        Limit Theorems continued...
27  Oct 31    4.3        Limits of Functions
28  Nov 2     4.3        Limits of Functions continued...
29  Nov 5     4.4        Consequences of Continuity
30  Nov 7                Review
31  Nov 9                Exam II
    Nov 12               Holiday (Veteran's Day)
32  Nov 14    4.4        Consequences of Continuity continued...
33  Nov 16    4.5        Uniform Continuity
34  Nov 19    4.5        Uniform Continuity continued...
35  Nov 21    4.6        Discontinuous and Monotone Functions
    Nov 23               Holiday (Thanksgiving)
36  Nov 26    5.1        The Derivative
37  Nov 28    5.2        Mean Value Theorems
38  Nov 30    5.3        Taylor's Theorem
39  Dec 3     5.3        Taylor's Theorem continued...
40  Dec 5     5.4        L'Hopital's Rule
41  Dec 7                Review
42  Dec 10               Review

Final Exam

• Section 001 on Monday, December 17 from 9:45 to 11:45am in AB 205.

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