Introduction to Mathematical Modeling
Fall 2023
Office Location:
Duke Hall #209
Phone: 909-748-8630
E-Mail: joanna_bieri@redlands.edu
(Email or Teams are my preferred contact methods)
Math Modeling Lab:
Wednesday 6-8pm Duke 206
Office Hours:
Make an Appointment:
Book an appointment on Calendly (click here)
This is where grades will be posted and announcements will be made.
- Important Course Documents
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Daily Course Documents
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Tuesday 8/29 - DAY 1
PROJECT 1 Assigned
Project 1 - DUE Thursday September 7th
Project Checklist
READING ASSIGNED - Please read the introduction to our text book (pages 1-7) and start brainstorming about all the things that could be modeled or described by mathematics.
Book - Introduction
HOMEWORK ASSIGNED: DUE Thursday 8/31 - DO THE EXERCISES on page 7 - Handwritten is fine.
*** BRING THIS TO NEXT CLASS
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Thursday 8/31 - DAY 2
HAND IN Homework 1 - problems from the book. These can be handwritten.
Make sure to be working with your group on Project 1. It is due Thursday 9/7.
Here is the example math modeling/ scientific paper that was handed out in class today. You should use this to help you think about how you might write up your group projects in a professional and clear way. CLICK HERE
OPTIONAL READING - Please read section 1.1 in our text book (pages 9-11). We will start working with reccurance relations next week!
NO NEW HOMEWORK - get ahead on Project 1. -
Tuesday 9/5 - DAY 3
Project 2 Due - Thursday 9/12 at 11:59pm.
Today Start Dynamical Models
Spreadsheet Formulas
Open Source Spreadsheet Program - Libre Office
Spreadsheet Example - In Class
Python Example - In Class - if time
HOMEWORK - Assigned today:
Homework 2 - Projecting into the Future - Due Tuesday 9/12
How To - Help with the Homework -
Thursday 9/7 - DAY 4 - Project 2 Assigned - Project 1 Due
Discrete Dynamical Population Models
Example Compartmental Diagram - from class
Project 2 - DUE Thursday Sept 21st
Project Checklist
SUBMIT PROJECT 1:
Project Self Assessment
SUMBIT PROJECT 1 HERE Let me know if you have trouble with this. It is my first time trying group project submissions on Canvas. If you run into trouble send me an email with your work.
HOMEWORK 3 - DUE TUESDAY 9/12 (Yes the same day as Homework 2)
Hand written is fine
1. Read through Project 2 - write up some brainstorming ideas for the project. This should include ideas for assumptions and compartmental diagrams. Think about problems that you might try to solve or issues that might arise.
2. Draw a draft compartmental diagram for the bobcat model that includes all the parts of the model from the prompt. Write down RECURRANCE relations from this model.
Reminder: Proposals for your final projects are due on Tuesday September 19th. Start working on this now.
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Tuesday 9/12 - DAY 5
Mathematical Analysis - Eigenvalues
Homework 4 - Due Tuesday 9/19.
Please read the whole document... notes on what exactly should be handed in are on page 2.
Example Eigenvalue Spreadsheet
Example Eigenvalue Python Code
Book Pages - Annual Plants
Reminder: Proposals for your final projects are due on Tuesday September 19th. Start working on this now. Come chat with me during lab if you are having a hard time coming up with an idea.
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Thursday 9/14 - DAY 6
Project 2 Due Next Thursday!
Final Project Proposals Due Next Tuesday 9/19 - Hand in on Canvas
Fixed Point Spreadsheet Example
Fixed Point Python Example
Example Cobweb Diagram
Example Cobweb Diagram
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Tuesday 9/19 - DAY 7 - Final Project Assumptions Due
Final Modeling Project Assumptions are due TODAY - These should be typed, please see the Final Project Deadlines for more information.
Logistic Equation Spreadsheet Example
In Class Project - Logistic Model - Not Handed In
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Thursday 9/21 - DAY 8 - Project 3 Assigned - Project 2 Due - CLICK HERE
Project Self Assessment
SUMBIT PROJECT 2 HERE by 11:59pm
Modeling Competition:
Host Parasite Model - In Class Example
Homework 5 - Math Models for Love - DUE Tuesday 9/26
Project 3 - Assigned
CHECK YOUR UNDERSTANDING - At this point in the semester you should be able to:
- Draw a compartmental diagram and write down the corresponding recurrence relations.
- Analyze the recurrence relations. Order, Linear or Nonlinear, Fixed Points, Stability, and in some cases Eigenvalues and Closed Form Solutions.
- Quickly program a spreadsheet to calculate values for a recurrence relation. Graph your solutions and test the sensitivity of a model.
- Define: Deterministic, Stochastic, Discrete, Continuous, Dynamic, and Static.
- Recognize the constant growth rate population model and the logistic population mode. Understand how we derive each of them.
COME GET HELP IF ANY OF THIS IS STILL HARD FOR YOU!!
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Tuesday 9/26 - DAY 9
You should be working on project 3 -- No New Homework
Lotka Volterra Model
Jupyter Notebook: Solve for Eigenvalues
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Thursday 9/28 - DAY 10
Reflect on the course so far... take time in class to work on Project 3. This project MUST contain some unique modeling or parameter analysis components!!
- Tuesday 10/3 - DAY 11
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Wednesday 10/4 - DAY 12 - Class during Lab Time
In Class Project - Monte Carlo Simulation
See if you can write your own code before clicking on these links ----------------------
Example Coin Flipping Spreadsheet
Python Code - Coin Flip
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You will need to use an official no-cloud version of Microsoft Excel OR you will need to write a Python Program!
Excel Functions and Formulas
NOTE: Final Project Updated Final Proposal - Due Tuesday October 17th
- Thursday 10/5 - Project 3 Due - No Class
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Fall Break
University Fall Break is Monday 10/9 and Tuesday 10/10. Our class will not meet on Wednesday 10/11 or Thursday 10/12. This means that you have a full week away from Math Modeling. Please take the time to rest your minds and get caught up if you need to. This is the perfect time to refocus on your final projects. See if you can get a first model codded up. -
Tuesday 10/17 - DAY 13 - Project 4 Assigned
Probability Distributions Spreadsheet
LA Rainfall Data
Example Spreadsheet - Histogram - Distributions
Project 4
REVIEW - Make sure to review basic statistics! You should be able to calculate and interpret the following things: Mean, Median, Mode, Histogram, 1st 2nd and 3rd Quartiles. Also make sure you can calculate these things using a spreadsheet.
Probability Distributions (pages 60-70) from our Book: Three Distributions
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Thursday 10/19 - DAY 14
Stochastic Cranes Handout
Stochastic Cranes Spreadsheet
You should be working with your group on Project 4!
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Tuesday 10/24 - DAY 15
Validity Testing Worksheet
Chi Squared Table
There are lots of resources online for more information about Chi Squared testing. -
Tuesday 10/26 - DAY 16
Project 4 due Tuesday 10/31
Use class today to work on Project 4. - Tuesday 10/31 - DAY 17 - Project 4 DUE
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Thursday 11/2 - DAY 18 - Project 5 Assigned
In Class Example - Age Class Model
Python Example - Population Eigenvalues and Eigenvectors.
This is the same file as we saw last class. We will edit this file in class today to model a population of nesting birds.
Project 5 - Due Thursday 11/16
Academic Paper for Project 5
- Tuesday 11/7 - DAY 19
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Thursday 11/9 - DAY 20
In Class Example - Markov Models
Final Project Meetings - Next week during class. -
Tuesday 11/14 - Thursday 11/16 - Individual Meetings for Final Projects
Thanksgiving Week - Keep working on your final projects!
Each day I will post the homework, additional reading, and additional information. Click on the links below to see the information for that day.
Upcoming schedule:
Tuesday 11/22 - No Class - Work on your final Project
Tuesday 11/28 - No Class - Joanna Office Hours - Come by during class for help on your final project.
Thursday 11/30 - LAST DAY - POSTER SESSION - Bring your poster and be prepared to present your final project.
Tuesday 12/5 - FINAL PROJECTS DUE - 11:59pm on Canvas. -
Tuesday 8/29 - DAY 1
Click on the link below to learn more about the final projects.
Final Project Deadlines
Final Project Information
Final Poster Information
Final Paper Checklist
SUMBIT FINAL PROJECTS HERE by 11:59pm
USE AT YOUR OWN RISK - There could be typos that are corrected in class, so please use common sense and your own notes to compare to what you see here:
Introduction - What is a mathematical model?
Definition of Terms - Example Model Taking a Hike
Introduction to Discrete Dynamical Systems - Projecting into the Future
Discrete Dynamical Population Models - More Compartmental Diagrams
Closed Form Solutions - Eigenvalues
Fixed Points and Stability
Non Constant Growth Rates - Logistic Equation
Systems of Recurrence Relations
Lotka Volterra Model - Continue Work on Project 3
Stochastic Modeling - Squirrels In Class Lab
In Class Lab - Monte Carlo Simulator
Probability Distributions and Stochastic Modeling
Validity Testing
Introduction to Stages, States, and Classes
Stages, States, and Classes - Eigenvalues and Freemat
More Examples of Stages, States, and Classes
Markov Models
Math Llamas LOVE group work!
Photo thanks to weruletheinternet.com
Photo thanks to weruletheinternet.com