Math 218, Spring 2023
Course Description
Instructor: Dr. Carissa Slone
Office Hours: Tuesdays, 2-4pm, in Hylan 820
Email: cslone2 (at) ur (dot) rochester (dot) edu
TA: Donovan Snyder
Email: dsnyd15 (at) u (dot) rochester (dot) edu
TA Office Hours: Wednesdays, 2:30-4pm, in Hylan 710. Zoom available, if requested over email.
Topics Covered: This course is aimed at building problem-solving ability in students through the development of mathematical models for certain real-life situations in the biological sciences. Models treated cover a variety of phenomena both discrete and continuous, linear and non-linear, deterministic and stochastic. Some topics that might be treated are Leslie Matrices in Demographics, Exponential and Logistic growth, Gompertz growth in tumors, Hardy-Weinberg Law in population genetics, Lotka-Volterra predator-prey systems, principle of competitive exclusion, the Kermack-McKendrick model of epidemics (and variants), Markov chain models (with the requisite intro to probability) and the stochastic pure birth process and epidemic models.
Homework: There will be weekly written homework assignments, due each Saturday at 6am on Gradescope. Some weeks there will also be WebWork assignments also due Saturday at 6am. Download the homework packet here or access the individual assignments here.
Online eigenvalue calculator: here.
Online phase plane plotter: here.
Exams:
Midterm -- in-class (B&L 270) on Tuesday, 2/28. (One double-sided 8.5x11in note sheet allowed, calculator allowed. Study guide.)
Final -- in-class (B&L 270) on Saturday, 5/6, at 8:30am. (One double-sided 8.5x11in note sheet allowed, calculator allowed. Study guide.)
Grading:
Written Homework 30%
WebWork 7.5%
Attendance 7.5%
Midterm Exam 25%
Final Exam 30%
Prerequisites: Math 143, or Math 162, or Math 172.
Homework Policy: Late homework will be accepted up to 6am on the following Monday (e.g., homework due 1/21 will be accepted up until 1/23). However, there will be a 50% reduction in the points earned on the homework (say 10 points are earned, then only 5 will be counted). There are no exceptions to this policy; any homework submitted past the late deadline will receive a 0. Homework will not be accepted over email.
Attendance Policy: Attendance is required and will be taken each class. This will be done via an iClicker quiz with location requirement enabled (i.e., you must be in the classroom to access the quiz). Any absences must be communicated before said absence. University approved absences (which are excused) must be accompanied by the appropriate documentation (e.g., doctor's note). Note that it is not possible to receive an A without attending class.
Disability Support: If you have an academic need related to a disability, arrangements can be made to accommodate most needs. For information please contact the Center for Excellence in Teaching and Learning. Note: To be granted alternate testing accommodations, you (the student) must fill out forms with CETL at least seven days before each and every exam. These forms are not sent automatically. Professors are not responsible for requesting alternative testing accommodations at CETL, and they are not obligated to make any accommodations on their own.
Academic Integrity Statement: You are responsible for knowing and abiding by the University of Rochester’s academic integrity code. For a complete listing visit the College of Arts, Sciences, and Engineering’s web site. Any violation of academic integrity will be pursued according to the specified procedures. In particular, submission of written work, including homework and exams, which has been copied from the work of other students (or anyone else) with or without their knowledge or consent, is plagiarism.
Schedule
Week of Jan 12 (Week 1):
Intro. to mathematical modeling.
Discrete linear, deterministic models.
Week of Jan 17 (Week 2):
Matrix algebra and eigenvalues.
Written homework 1 due, Saturday, 1/21, at 6am.
Week of Jan 24 (Week 3):
Demographics and Leslie matrices.
Hardy-Weinberg law of genetics.
Written homework 2 due, Saturday, 1/28, at 6am.
WeBWork homework 1 due, Saturday, 1/28, at 6am.
Week of Jan 31 (Week 4):
Continuous, linear, deterministic models.
Written homework 3 due, Saturday, 2/4, at 6am.
Week of Feb 7 (Week 5):
Exponential growth, logistic growth models.
The Allee effect model.
Steady states, phase lines, and stability analysis.
Written homework 4 due, Saturday, 2/11, at 6am.
WeBWork homework 2 due, Saturday, 2/11, at 6am.
Week of Feb 14 (Week 6):
Complex eigenvalue problems.
Linear systems of differential equations.
Phase portraits.
Written homework 5 due, Saturday, 2/18, at 6am.
WeBWork homework 3 due, Saturday, 2/18, at 6am.
Week of Feb 21 (Week 7):
Non-linear systems; steady-states, linearization/Jacobian, and stability.
Non-linear systems; nullclines, direction of solution curves.
Written homework 6 due, Saturday, 2/25, at 6am.
WeBWork homework 4 due, Saturday, 2/25, at 6am.
Week of Feb 28 (Week 8):
Predator-prey systems, Lotka-Voltera equations.
Competitive species and the principle of competitive exclusion.
MIDTERM EXAM -- TUESDAY, 2/28. IN-CLASS.
Covers weeks 1-5.
Week of Mar 7 (Week 9):
SPRING BREAK.
Week of Mar 14 (Week 10):
CLASS ONLINE THIS WEEK (see Blackboard for Zoom link).
Compartment models in Epidemiology.
SIR-model of Kermack-McKendrick.
Week of Mar 21 (Week 11):
CLASS IN-PERSON.
Herd immunity.
SIR-model with vital dynamics.
Basics of probability.
Written homework 7 due, Saturday, 3/25, at 6am.
Week of Mar 28 (Week 12):
Conditional probability, Bayes’ theorem, independence.
Bernoulli processes
Random variables, expectation, variance.
Written homework 8 due, Wednesday, 4/5, at 6am.
Week of Apr 4 (Week 13):
Markov chains.
Written homework 9 due, Wednesday, 4/12, at 6am.
Week of Apr 11 (Week 14):
Absorbing Markov chains.
Written homework 10 due, Saturday, 4/15, at 6am.
Week of Apr 18 (Week 15):
Absorbing Markov chains continued.
Written homework 11 due, Saturday, 4/22, at 6am.
Week of Apr 25 (Week 16):
Final exam review.
FINAL EXAM (covers weeks 6-15) -- Saturday, 5/6, at 8:30am