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 2005

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 10:00-10:50am AB 209

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 29    1.1        Proofs
2   Aug 31    1.2        Sets
3   Sep 2     1.3        Functions
    Sep 5                Holiday
4   Sep 7     1.4        Mathematical Induction
    Sep 8                Final date for withdrawing with refund
5   Sep 9     2.1        Algebraic and Order Properties of R
6   Sep 12    2.2        The Completeness Axiom
7   Sep 14    2.3        The Rational Numbers are Dense in R
8   Sep 16    2.4        Cardinality
9   Sep 19    3.1        Convergence
10  Sep 21    3.2        Limit Theorems
11  Sep 23    3.3        Subsequences
12  Sep 26    3.4        Monotone Sequences 
13  Sep 28    3.4        Monotone Sequences continued...
14  Sep 30    3.5        Bolzano-Weierstrass Theorems 
15  Oct 3     3.5        Bolzano-Weierstrass Theorems continued...
16  Oct 5     3.6        Cauchy Sequences 
17  Oct 7                Review
18  Oct 10               Exam I
19  Oct 12    3.7        Limits at Infinity 
20  Oct 14    3.8        Limit Superior and Limit Inferior 
21  Oct 17    4.1        Continuous Functions 
22  Oct 19    4.2        Limit Theorems  
23  Oct 21    4.3        Limits of Functions  
                         Final date for dropping class no refund
24  Oct 24    4.4        Consequences of Continuity  
25  Oct 26    4.4        Consequences of Continuity continued...
    Oct 28               Holiday
26  Oct 31    4.5        Uniform Continuity 
27  Nov 2     4.6        Discontinuous and Monotone Functions 
28  Nov 4     5.1        The Derivative 
29  Nov 7                Review
30  Nov 9                Exam II
    Nov 11               Holiday
31  Nov 14    5.2        Mean Value Theorems 
32  Nov 16    5.2        Mean Value Theorems continued...
33  Nov 18    5.3        Taylor's Theorem  
34  Nov 21    5.3        Taylor's Theorem continued...
35  Nov 23    5.4        L'Hopital's Rule
    Nov 25               Holiday
36  Nov 28    6.1        Existence of Riemann Integral
37  Nov 30    6.2        Riemann Sums
38  Dec 2     6.2        Riemann Sums continued...
39  Dec 5     6.3        Properties of the Riemann Integral
40  Dec 7     6.4        Families of Riemann Integrable Functions
41  Dec 9                Review
42  Dec 12               Review

Final Exam

• Section 001 on Friday, Dec 16 from 9:45 to 11:45am in AB 209.

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