Math 420

Spring 2026 University of Nevada Reno

420 MATHEMATICAL MODELLING (3+0) 3 credits

Formulation, analysis and critique of methods of mathematical modeling; selected applications in physics, biology, economics, political science and other fields. MATH 283 and MATH 285 both with a C or better; STAT 352 or STAT 461 either with a C or better. 

Instructor  Course Section                     Time              Room
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Eric Olson  Math 420 Mathematical Modeling     MWF 10-10:50am    PE104

Course Information

Instructor:
Eric Olson
email:
Please contact me through WebCampus
Office:
MWF 12:30-1:30pm in DMS 238 and through Zoom by appointment
Homepage:
http://fractal.math.unr.edu/~ejolson/285/

Course Textbook:
Mark Meerschaert, Mathematical Modeling, 4th Edition, 2013, Elsevier.

Additional Resources:
Consortium for Mathematics and its Applications
SIAM Math Modeling Challenge

Student Learning Outcomes

We will cover selected sections in Chapters 1 through 5, 7 and 8 of the textbook. Upon completing this course, a student shall be able to

Information about Software

I will occasionally use the Julia programming language in class to draw graphs and perform simple calculations. This software is free to download for Windows, MacOS and Linux.

Class Handouts

Course materials specific for this section of Math 420 are available by clicking on this link. Details for how to access these files may be found on our course page in WebCampus.

Homework

This homework is to help prepare you for the quizzes. Quiz 1 fill focus on Homework 1, Quiz 2 will focus on Homework 2 and so forth. The homework corresponding to each quiz will not be collected or graded.

Homework 1
Section 1.4#1,2,3
Homework 2
Section 2.4#1,2
Homework 3
Section 2.4#6,7
Homework 4
Section 3.5#1,2
Homework 5
Section 3.5#6,11
Homework for Midterm
Section 3.5#15,17,19
Homework 6
Section 4.4#4,5
Section 5.4#1(a-c),2(a-c)
Homework 7
Section 4.4#11
Section 5.4#12,13,14,15
Homework 8
Section 6.5#1,2,3
Homework 9
Section 6.5#15,16,17,19,20
Homework for Exam 2
Section 7.5#1,2,3
Homework 10
Section 7.5#5,6,11,12
Homework for Final
Section 8.5#5,6,9,10

Lecture Notes

Announcements

[09-May-2026] Project Solutions

I have worked each of versions done by the groups and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[13-May-2026] Final Exam Due

Turn in a paper version of your work to the Department of Mathematics and Statistics located on the third floor of the DMSC building by noon on May 13. Ask the person at the window in the hallway to put your work in Eric Olson's mailbox. Please do not turn in your work late, because the department office may close.

[08-May-2026] Final Exam

Projects will be due May 8 at 10:15am at the scheduled final exam. Turn in only one report per group and clearly indicate who was in the group. I will also hand out a take-home final exam at the scheduled final on May 8 at 10:15am. Your solutions to the final exam will be due the following week on May 13.

[06-May-2026] Quiz 10 Solutions

I have worked Quiz 10 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[28-Apr-2026] Exam 2 Solutions

I have worked Exam 2 and obtained the solutions to question 1 (ipynb), question 2 (ipynb) and question 3 (ipynb). Please let me know if you see any errors or ways I could improve things.

[27-Apr-2026] Class Projects

Projects will be similar to the quizzes and exams except that you may work in groups from 1 to 3 people. Each group will have a slightly different project. I have printed out copies of the different project versions and will bring them to class this week starting Monday. Please think about forming your group and pick up the project assignment for your group this week.

[18-Apr-2026] Quiz 9 Solutions

I have worked Quiz 9 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[14-Apr-2026] Quiz 8 Solutions

I have worked Quiz 8 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[04-Apr-2026] Quiz 7 Solutions

I have worked Quiz 7 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[04-Apr-2026] Quiz 6 Solutions

I have worked Quiz 6 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[07-Mar-2026] Midterm Solutions

I have worked the midterm and obtained the solutions to question 1 (ipynb), question 2 (ipynb) and question 3 (ipynb). Please let me know if you see any errors or ways I could improve things.

[07-Mar-2026] Quiz 5 Solutions

I have worked Quiz 5 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[03-Mar-2026] Quiz 4 Solutions

I have worked Quiz 4 and obtained these solutions. You can also download the JupyterLab worksheet. Please let me know if you see any errors or ways I could improve things.

[18-Feb-2026] Snow Day

Following an assessment of the anticipated overnight weather and road conditions around the University of Nevada, Reno campus, nonessential campus operations and in person classes are suspended today.

[14-Feb-2026] Quiz 3 Solutions

I have worked Quiz 3 and obtained these solutions. You can also download the Pluto worksheet. Please let me know if you see any errors or ways I could improve things.

[06-Feb-2026] Quiz 2 Solutions

I have worked Quiz 2 and obtained these solutions. Please let me know if you see any errors or ways I could improve things.

[21-Jan-2026] Welcome Spring 2026

I am looking forward to seeing you January 26 starting the first week of class.

In person attendance is mandatory for all computing labs, quizzes, exams and the final.

Grading

     2 Exams                   50 points each
     10 Quizzes                10 points each
     Project                   25 points
     Final                    100 points
    ------------------------------------------
                              325 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 it is believed they are warranted.

Calendar


Jan 21    1.1         The Five-step Method
Jan 23    1.2         Sensitivity Analysis

Jan 26    1.3         Sensitivity Analysis
Jan 28    1.3         Sensitivity Analysis (quiz 1)
Jan 30    2.1         Unconstrained Optimization

Feb 2     2.1         Unconstrained Optimization
Feb 4     2.2         Lagrange Multipliers (quiz 2)
Feb 6     2.2         Lagrange Multipliers 

Feb 9     2.3         Sensitivity Analysis and Shadow Prices
Feb 11    2.3         Sensitivity Analysis and Shadow Prices (quiz 3)
Feb 13    3.1         One Variable Optimization

Feb 16    President's Day
Feb 18    3.1         One Variable Optimization
Feb 20    3.2         Multivariable Optimization
            
Feb 23    3.2         Multivariable Optimization
Feb 25    3.3         Linear Programming (quiz 4)
Feb 27    3.3         Linear Programming

Mar 2     3.4         Integer Programming
Mar 4     3.4         Integer Programming (quiz 5)
Mar 6     4.1         Steady State Analysis

Mar 9     Review
Mar 11    EXAM 1
Mar 13    4.2         Dynamical Systems 

Mar 16    4.3         Discrete Time Dynamical Systems 
Mar 18    5.1         Eigenvalue Methods (quiz 6)
Mar 20    5.1         Eigenvalue Methods

Mar 23    Spring Break
Mar 25    Spring Break
Mar 27    Spring Break

Mar 30    5.2         Eigenvalue Methods for Discrete Systems
Apr 1     5.3         Phase Portraits (quiz 7)
Apr 3     6.1         Introduction to Simulation

Apr 6     6.2         Continuous-Time Models
Apr 8     6.3         The Euler Method (quiz 8)
Apr 10    6.4         Chaos and Fractals

Apr 13    7.1         Discrete Probability Models
Apr 15    7.2         Continuous Probability Models (quiz 9)
Apr 17    7.3         Introduction to Statistics

Apr 20    Review
Apr 22    EXAM 2             
Apr 24    8.1         Markov Chains

Apr 27    8.1         Markov Chains
Apr 29    8.2         Markov Processes (quiz 10)
May 1     8.3         Linear Regression

May 4     8.3         Linear Regression

May 8     Final Exam at 10:15-12:15pm

Course Policies

Communications Policy

Lectures and classroom activities will held in person. If you wish to set up an appointment for office hours please send me a message through WebCampus.

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.

AI Policy

In this course you are welcome to use generative artificial intelligence/large language model tools (such as ChatGPT, Claude, Gemini, Grok, Perplexity, etc.). Using these tools aligns with the course learning outcomes/student goals for an in-depth understanding of mathematical modeling.

Please be aware that many AI companies collect and store personal information. Please do not enter your confidential information as part of a prompt.

Also, please note that some of these large language models may make up or hallucinate information. These tools may reflect misconceptions and biases of specific data. Students are responsible for checking facts, finding reliable sources for, and making a critical examination of any work that is submitted.

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, generative AI such as ChatGPT as well as personal communications. Note that answers obtained from any source should be verified and fully understood for homework to have a positive learning outcome. In all cases your sources need to be cited.

Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work.

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, generative AI such as ChatGPT as well as personal communications. Note that answers obtained from any source should be verified and fully understood for homework to have a positive learning outcome. In all cases your sources need to be cited.

Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work.

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 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.

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.

Statement on Academic Success Services

Your student fees cover usage of the University Math Center, (775) 784-4433; University Tutoring Center, (775) 784-6801; and University Writing & Speaking Center, (775) 784-6030. 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.

Statement of Disability Services

Any student with a disability needing academic adjustments or accommodations is requested to speak with me or the Disability Resource Center (Pennington Achievement Center Suite 230) as soon as possible to arrange for appropriate accommodations. This course may leverage 3rd party web/multimedia content, if you experience any issues accessing this content, please notify your instructor

Mental Health Support Statement

There are times when you may experience difficulties in life, and you may benefit from seeking help. Mental health services are available to you as a student at no additional cost through Counseling Services at the Pennington Student Achievement Center. This includes same-day in-person and tele mental health initial consultations, brief individual counseling, and group counseling sessions. Limited same-day appointments can be scheduled online via Counseling Services or by calling 775-784-4648. Additional brief drop-in "Let's Talk" student consultations are also available in the Counseling Services Annex located at the southwest corner of Great Basin Hall.

Veteran Statement

Veterans, Reservists, National Guard and military connected family members may wish to check the office of Veteran Services for benefits and support. Besides processing VA educational benefits, the department offers a variety of programs year-round to support student academic and personal success while transitioning to higher education and throughout your educational experience. They welcome inquiries regarding VA benefits and assist in navigating resources, the campus, and in the Reno community.

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.

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 Friday, May 8, 2026 from 10:15-12:15pm in PE104.
Last Updated: Tue Jan 20 08:37:10 PM PST 2026