Mathematics 310 Homepage

Spring 2024 University of Nevada Reno

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.

Instructor  Course Section                       Time
------------------------------------------------------------------------
Eric Olson  001 Math 310 INTRO TO ANALYSIS I     MWF 9:00-9:50am PE103

Course Information

Instructor:
Eric Olson
email:
Please contact me through WebCampus
Office:
DMS 238 MW from 11am to 1pm
Homepage:
https://fractal.math.unr.edu/~ejolson/310/
Live Stream:
If you can't come to class due to sickness, quarantine or other reasons, please join via the Zoom link in WebCampus.

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

Other Reading:
Joseph Taylor, Foundations of Analysis, Twelfth Edition, American Mathematical Society, 2012.

Jay Cummings, Real Analysis, A Long-Form Mathematics Textbook, 2019.

Gerald Folland, Advanced Calculus, First Edition, Pearson.

Walter Rudin, Principles of Mathematical Analysis, Third Edition, McGraw-Hill, 1976.

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

Student Learning Outcomes

Upon completion of this course, students will be able to

Class Handouts

Course materials specific for this section of Math 310 are available by clicking on this link. Details for how to access these files may be found on our course page in WebCampus.

Homework

Lecture Notes

Announcements

[15-May-2024] Final Exam

The final exam will be Wednesday, May 15 from 8:00-10:00am in PE103. I have posted a sample final exam to help to study.

Please review the following in preparation:

  1. All definitions from
  2. The homework problems.
  3. Know the proofs of
  4. Be able to state (without proof) exactly
  5. Examples

[03-May-2024] Quiz 5

There will be a short quiz in class on Friday, May 3 covering homework 8.

[15-Apr-2024] Exam 2

There will be an exam in class on Monday, Apr 15 covering

[06-Apr-2024] Homework 7 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[16-Mar-2024] Homework 6 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[06-Mar-2024] Exam 1 (rescheduled)

There will be an exam in class on Wednesday, Mar 6 covering

[04-Mar-2024] Exam 1 (cancelled due to snow)

There will be an exam in class on Monday, Mar 4 covering

[02-Mar-2024] Homework 5 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[01-Mar-2024] Quiz 2

There will be a short quiz in class on Friday, Mar 1 covering the first four homework assignments as well as the definitions appearing in the book up to Chapter 3.2.

[20-Feb-2024] Homework 4 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[20-Feb-2024] Homework 3 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[16-Feb-2024] Quiz 1

There will be a short quiz in class on Friday, Feb 16 covering the first two homework assignments.

[12-Feb-2024] Homework 2 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[08-Feb-2024] Homework 1 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[19-Jan-2024] Welcome Spring 2024

I am looking forward to seeing you starting the first week of class.

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.

Do not come to class if you are sick--even if it's something other than COVID-19. If you are subject to quarantine because of exposure to a person who is sick, please stay home.

This section of Math 310 is in person. However, I will live-stream our class meetings each day at a link available in WebCampus for those who are sick or unable to attend on a particular day. I will also maintain an online archive of course materials including lecture notes, assignments and other announcements.

Tentative Course Schedule

#   Date     Chapter     Topic
------------------------------------------------------------------------
1   Jan 22    1.1        Proofs
2   Jan 24    1.2        Sets
3   Jan 26    1.3        Functions

4   Jan 29    1.4        Mathematical Induction
5   Jan 31    2.1        Algebraic and Order Properties of R
6   Feb 02    2.1        Properties of R continued...

7   Feb 05    ***        Snow Day
8   Feb 07    2.2        The Completeness Axiom
9   Feb 09    2.3        The Rational Numbers are Dense in R

10  Feb 12    2.4        Cardinality
11  Feb 14    2.4        Cardinality continued...
12  Feb 16               Quiz 1

    Feb 19    ***        President's Day
13  Feb 21    3.1        Convergence
14  Feb 23    3.2        Limit Theorems

15  Feb 26    3.3        Subsequences
16  Feb 28    3.4        Monotone Sequences
17  Mar 01    3.4        Monotone Sequences continued...

18  Mar 04               Exam I
19  Mar 06    3.5        Bolzano-Weierstrass Theorems
20  Mar 08    3.5        Bolzano-Weierstrass continued...

21  Mar 11    3.6        Cauchy Sequences
22  Mar 13    3.7        Limits at Infinity
23  Mar 15    3.8        Limit Superior and Limit Inferior

24  Mar 18    4.1        Continuous Functions
25  Mar 20    4.2        Limit Theorems
26  Mar 22    4.3        Limits of Functions

*** Spring Break Saturday Mar 23 to Sunday March 31

27  Apr 01    4.4        Consequences of Continuity
28  Apr 03    4.4        Consequences of Continuity continued... 
29  Apr 04    4.5        Uniform Continuity

30  Apr 08    4.6        Discontinuous and Monotone Functions
31  Apr 10    5.1        The Derivative
32  Apr 12    5.2        Mean Value Theorems

33  Apr 15               Exam II
34  Apr 17    5.3        Taylor's Theorem
35  Apr 19    5.3        Taylor's Theorem continued...

36  Apr 22    5.4        L'Hopital's Rule (skipped)
37  Apr 24    6.1        Existence of Riemann Integral
38  Apr 26    6.2        Riemann Sums

39  Apr 29    6.3        Properties of the Riemann Integral
40  May 01    6.3        Riemann Integral continued...
41  May 03    6.4        Families of Riemann Integrable Functions

42  May 06    ***        Review

*** Prep Day May 08
*** Final exam Wednesday, May 15 from 8:00-10:00am in PE103

Grading

     2 Exams                   50 points each
     5 Quizzes                  5 points each
     5 Homework Assignments     5 points each
     Final Exam               100 points
    ------------------------------------------
                              250 points total
Exams and quizzes will be interpreted according to the following grading scale:
    Grade        Minimum Percentage
      A                 90 %
      B                 80 %
      C                 70 %
      D                 60 %
The instructor reserves the right to give plus or minus grades and higher grades than shown on the scale if he believes they are warranted.

Quiz and Exam Schedule

There will be two quizzes, a midterm and a final exam. In person attendance is mandatory for all exams.

Course Policies

Communications Policy

Lectures and classroom activities will held in person and live streamed through through Zoom at the scheduled meeting time listed in MyNevada for this course. Please check the canvas page for the Meeting ID and Join URL under the Zoom tab if you are unable to make it to class. If you wish to set up an appointment for office hours please send me a message through WebCampus. I am available to meet in my office or through Zoom.

Late Policy

Students must have an approved university excuse to be eligible for a make-up exam. If you know that you will miss a scheduled exam please let me know as soon as possible.

Plagiarism

Students are encouraged to work in groups and consult resources outside of the required textbook when doing the homework for this class. Please cite any sources you used to complete your work including Wikipedia, other books, online discussion groups as well as personal communications. Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work. Please consult the section on academic conduct below for additional information.

Diversity

This course is designed to comply with the UNR Core Objective 10 requirement on diversity and equity. More information about the core curriculum may be found in the UNR Catalog here.

Statement on Academic Success Services

Your student fees cover usage of the University Math Center, University Tutoring Center, and University Writing and Speaking Center. These centers support your classroom learning; it is your responsibility to take advantage of their services. Keep in mind that seeking help outside of class is the sign of a responsible and successful student.

Equal Opportunity Statement

The University of Nevada Department of Mathematics and Statistics is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to speak with the Disability Resource Center during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments. For assistance with accessibility, or to report an issue, please use the Accessibility Help Form. The form is set up to automatically route your request to the appropriate office that can best assist you.

Statement on Audio and Video Recording

Surreptitious or covert video-taping of class or unauthorized audio recording of class is prohibited by law and by Board of Regents policy. This class may be videotaped or audio recorded only with the written permission of the instructor. In order to accommodate students with disabilities, some students may be given permission to record class lectures and discussions. Therefore, students should understand that their comments during class may be recorded.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't send electronic messages, talk or pass notes with other students during a quiz or exam. Homework may be discussed freely. When taking a quiz, midterm or exam don't read notes or books unless explicitly permitted. Sanctions for violations are specified in the University Academic Standards Policy. If you are unclear as to what constitutes cheating, please consult with me.

Final Exam

The final exams will be held in person at the time listed in the standard schedule of final exams for this section. Namely, the final exam is Wednesday, May 15 from 8:00-10:00am in PE103.
Last Updated: Fri Jan 19 09:52:14 AM PST 2024