Eli Goldwyn

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Calculus 1 Exam Page

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Exam 1:

  • Sections 1.7-2.5
  • Review Topics and Preparation Hints (pdf)
  • Practice Problems (pdf) (SOLUTIONS)
  • Previous Exams:

Exam 2 (Chapters 3 & 4)

  • Chapter 3

Final:

 

 

 

OLD INFORMATION!

Exam 2:

  • Chapter 3
  • Review Topics and Preparation Hints (pdf)
  • Practice Problems  (pdf) (SOLUTIONS)
  • Previous Exams:

Exam 3:

Syllabus (131)

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Math 131 – Calculus I, Fall 2016          

SYLLABUS

Instructor:                  Eli Goldwyn
Office Location:         MECC 265
Office Hours:            click “HOME” link above
Email:                          eli.goldwyn(at)trincoll.edu (please include “MATH 131” in the subject line!!!)

taalman

Class Meeting Time:

  • MWF  12:00-12:50           Room: SH-N129
  • Thur   10:50-12:05           Room: MECC 172

Textbook (the same book is used for Calculus I, II, and III):

  • Calculus by Laura Taalman and Peter Kohn
  • Online HW through WebAssign
    • Use class key: trincoll 3939 9988
      • Purchasing the book at the bookstore comes with access to WebAssign
      • If you purchase the book elsewhere and it doesn’t come with WebAssign, you can purchase access to WebAssign.
      • If you dont want a physical copy of the book, you can purchase the Ebook and access to WebAssign together at WebAssign.net.

Course Outline (detailed google doc):

  • Pre-calculus review (1 week)
  • Limits
    • Intuitive Limits
    • Definition
    • Limit Rules
    • Indeterminate Limits
    • Continuity
  • Derivatives
    • Intuitive Derivatives
    • Definition of Derivative
    • Derivative Rules
    • Chain, Product, and Quotient Rules
    • Implicit Differentiation
    • Derivatives of Exponential, Logarithmic, and Trigonometric Functions
    • Mean Value Theorem
    • Using First and Second Derivatives for Curve Sketching
    • Related Rates
    • L’Hopital’s Rule
  • Differential Equations
    • Slope Fields
    • Euler’s Method

Applications:

  • Mechanics (position, velocity, acceleration)
  • Population Growth/Decay
  • Newton’s Law of Cooling
  • Mean Value Theorem
  • Optimization Problems
  • Related Rates
  • Root Finding (Newton’s Method)
  • Numerical Approximation of Differential Equations (Euler’s Method)

Grading:

  • Homework (written and online)                                        20%
  • Quizzes                                                                                    10%
  • Midterms  (Oct 6, Nov 3, Dec 1. 7:00-8:30 PM)           45%      (15% each)
  • Final Exam (cumulative) (schedule)                             25%

Homework

  • Written Homework is due BEFORE class starts every Thursday. It will be graded on both the mathematical content and on the exposition, where appropriate (the correct answer may not be enough). I encourage you to work together, but you must submit your own work. If your HW is multiple pages, staple pages together. If you use spiral notebook paper, remove fringes (you will lose points if you fail to do this — I know it’s annoying but otherwise grading the HW becomes impossible)! Your lowest  HW score will be dropped.
  • Online Homework will be due a few days after we finish each section – several times per week (due dates and time will be either Monday, Wednesday, or Friday at midnight).  It will be assigned and graded through the online WebAssign system. I will announce the HW in class or over email and you can double check at WebAssign. If you have a question about the grade on a particular assignment, send me an email including the number of the assignment and problem as well as a screenshot of the problem with your answer.
  • Note: While all HW can be done open book/notes/internet and with classmates, if you need any of those resources to complete a problem, then you don’t really understand it. Be sure to practice some problems without any assistance- as if they are exam problems.
  • Late HW will NOT be accepted.

Quizzes will be given once a week (on Thursdays), will be based on that week’s (written) HW and will be 10-15 minutes. Your lowest quiz score will be dropped.

Exams: There will be three regular exam and a cumulative final exam. Make up exams are given only in the case of a serious medical problem or emergency documented by the Dean of Students office. Written documentation any such situation will be required. Advanced notice must be given if possible.

  • Calculator Policy: Calculators will NOT be allowed on quizzes or exams.
  • Exam Regrade Policy: If you think your exam was misgraded (I mis-added your points, I marked you wrong when your answer was correct, or you think you deserve more partial credit), you can return your exam to me with a letter (less than 1 page – can be handwritten neatly or printed out and signed in pen) describing why you deserve more points. You have one week from after I return the exams to submit this letter to me. Be sure to make this letter convincing.  Note: you can only do this one time per exam, so make sure you go through your entire exam BEFORE completing the above process.

Specific Classroom Rules:

  • You are expected to arrive for class on time and prepared, having completed any required reading and/or homework.
  • Cell phone use is for emergencies only! You can wait until after class to play. Please make sure your phone is off or on airplane mode!

Study Hints:

  • Come to class (and ask questions if you don’t understand).
  • Read the book BEFORE class.
  • Help each other (explaining a concept is a great way to understand it).
  • Attend my office hours and/or TA sessions, and visit the Q-center for tutoring/group work.
  • Review your class notes (I recommend doing this the same day).
  • Practice some HW or examples w/o friends or the book
  • Be patient! It’s okay if you don’t understand a concept the first time you see it.
  • VOX.com tips for “studying smarter”
  • The rule of thumb is that for every hour of class, you should spend ~3 hours outside of class.

You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

  • Click here for a cool TEDx video (“Being a fantastic educator: a lesson from my niece”) about teaching that generally sums up my teaching philosophy (by coincidence the speaker is my college roommate’s younger brother).

Students with Academic Accommodations: Trinity College complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act.  If you have a documented disability and require academic accommodations, please present your accommodations letter during my office hours within the first two weeks of the semester. If you do not have a letter, but have questions about applying for academic accommodations, please contact Lori Clapis, Coordinator of Accommodation Resources, at 860-297-4025 orLori.Clapis@trincoll.edu. You are responsible for reminding me about your accommodation 1 week before each exam.

Academic Honesty: Academic integrity is an important component of intellectual life and I treat cases of academic dishonesty very seriously. You are expected to uphold the principles in the Student Integrity Contract, to read and abide by the College policies on intellectual honesty in the Student Handbook, and to abide by any specific policies I establish. You will receive these policies in writing. If you have any questions you should bring them to me; when in doubt err on the side of caution and avoid even the appearance of academic dishonesty. The minimum penalty for academic dishonesty is a 0 on the given assignment. All cases of academic dishonesty will be referred to the Academic Honor Council.

Syllabus (252)

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Math 252, Spring 2016          

SYLLABUS

Instructor:                  Eli Goldwyn
Office Location:         MECC 265
Office Hours:            click “HOME” link above
Email:                          eli.goldwyn@trincoll.edu (please include “MATH 252” in the subject line!!!)

imagesClass Meeting Time:    MW 2:40-3:55           Room: MECC 260

Textbooks:

  • Mathematical Methods in Biology by J. David Logan and William R. Wolesensky (amazon link)

 

Course Description:  Application of elementary mathematics through first-year calculus to the construction and analysis of mathematical models. Applications will be selected from the natural sciences and social sciences, with an emphasis on the natural sciences. Several models will be analyzed in detail, and the computer will be used as necessary. The analysis will consider the basic steps in mathematical modeling: recognition of the non-mathematical problem, construction of the mathematical model, solution of the resulting mathematical problems, and analysis and application of the results

Grading:

  • Attendance/Participation                                                 5%
  • Homework (written and computational)                      30%
  • Exam (Wednesday 3/30)                                                  15%
  • Projects  (rough draft due: 4/20, final due: 5/2)         20%
  • Final Exam (cumulative) (schedule)                            30%

Homework (due every Wednesday unless otherwise specified):

  • Homework is due weekly(ish) and will be graded on both the mathematical content and on the exposition, where appropriate (the correct answer may not be enough). Homework will include written and computational (Matlab) problems. I encourage you to work together, but you must submit your own work. These problems will be posted on the course website and will turned in before class each Wednesday. If your HW is multiple pages, staple pages together. If you use spiral notebook paper, remove fringes (you will lose points if you fail to do this — I know it’s annoying but otherwise grading the HW becomes impossible)!
  • Note: While all HW can be done open book/notes/internet and with classmates, if you need any of those resources to complete a problem, then you don’t really understand it. Be sure to practice some problems without any assistance- as if they are exam problems.

Exams: There will be one regular exam and a cumulative final exam. Make up exams are given only in the case of a serious medical problem or emergency documented by the Dean of Students office. Written documentation any such situation will be required. Advanced notice must be given if possible.

  • Exam Regrade Policy – If you think your exam was misgraded (I mis-added your points, I marked you wrong when your answer was correct, or you think you deserve more partial credit), you can return your exam to me with a letter (less than 1 page – can be handwritten neatly or printed out and signed in pen) describing why you deserve more points. You have one week from after I return the exams to submit this letter to me. Be sure to make this letter convincing.  Note: you can only do this one time per exam, so make sure you go through your entire exam BEFORE completing the above process.

Projects: There will be one projects. I will provide a short list of topics for the project (you are more than welcome to come up with your own ideas, though you need to clear it with me first). In general you will modify (or create) and describe an existing model and analyze its behavior. The projects will require a first draft (worth 20%) and a final draft.

Specific Classroom Rules:

  • You are expected to arrive for class on time and prepared, having completed any required reading and/or homework.
  • Cell phone use is for emergencies only! You can wait until after class to play. Please make sure the ringer is off!

Study Hints:

  • Come to class (and ask questions if you don’t understand).
  • Read the book BEFORE class.
  • Help each other (explaining a concept is a great way to understand it).
  • Attend my office hours and/or TA sessions, and visit the Q-center.
  • Review your class notes (I recommend doing this the same day).
  • Practice some HW or examples w/o friends or the book
  • Be patient! It’s okay if you don’t understand a concept the first time you see it.
  • VOX.com tips for “studying smarter”
  • The rule of thumb is that for every hour of class, you should spend ~3 hours outside of class.

You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

  • Click here for a cool TEDx video (“Being a fantastic educator: a lesson from my niece”) about teaching that generally sums up my teaching philosophy (by coincidence the speaker is my college roommate’s younger brother).

Applications

  • Foraging Theory
  • Heat Transfer
  • Population Dynamics
  • Stage/Age Structured Population Dynamics
  • Interacting Population Dynamics
  • Birth/Death Processes
  • Disease Outbreaks

Mathematical Topics

  • Differential Equations
  • Difference Equations
  • Taylor Series
  • Non-dimensionalization
  • Regression and Curve Fitting
  • Matrices and eigenvectors/eigenvalues
  • Phase-plane (null-cline) analysis
  • Random Numbers and Random Walks

Students with Academic Accommodations: Trinity College complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act.  If you have a documented disability and require academic accommodations, please present your accommodations letter during my office hours within the first two weeks of the semester. If you do not have a letter, but have questions about applying for academic accommodations, please contact Lori Clapis, Coordinator of Accommodation Resources, at 860-297-4025 orLori.Clapis@trincoll.edu.

Academic Honesty: Academic integrity is an important component of intellectual life and I treat cases of academic dishonesty very seriously. You are expected to uphold the principles in the Student Integrity Contract, to read and abide by the College policies on intellectual honesty in the Student Handbook, and to abide by any specific policies I establish. You will receive these policies in writing. If you have any questions you should bring them to me; when in doubt err on the side of caution and avoid even the appearance of academic dishonesty. The minimum penalty for academic dishonesty is a 0 on the given assignment. All cases of academic dishonesty will be referred to the Academic Honor Council.

Syllabus (325)

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Course: MATH 325 Special Topics in Math Bio, Fall 2015
Time and Location: Monday and Friday 1:15 – 02:30pm MECC 293
Professor: Eli Goldwyn   eli.goldwyn@trincoll.edu (please include “math325” in the subject line)

Description: Introduction to developing, simulating, and applying dynamic models in biology. Students will also learn to construct and study dynamic models on the computer using Matlab (or R).

Textbook: Dynamic Models in Biology by S.P. Ellner and J. Guckenheimer, Princeton University Press (2006). Supplementary readings will be made available through the course website. j8124

Topics: Tried and true modeling approaches with wide applicability and enduring utility. Simple models of real biology, classic and current.

  • What are dynamic models?
  • Matrix models for structured populations
  • Neurobiology: membrane channels & action potentials
  • Cellular dynamics: gene expression
  • Dynamical systems
  • Infectious diseases
  • Spatial pattern formation

Grading

  • Participation: (5%) Attend class, ask questions, and participate in discussion
  • Lead class: (5%) Each student will lead class for a day. This will include preparing notes to teach the mathematical topic and leading a discussion.
  • Homework: (25%). HW will include theoretical problems, computation problems, and written work.
  • Two exams. (20% each) The first will be in class. The second will be take-home. Dates are TBD.
  • Term project (25%): this will involve taking a modeling paper in in an area of biology that interests you, and carrying the research a small step forward. We will help you to identify a good topic and will consult closely with you during your first steps as a computational biologist. A description of the term project is posted on the course website.

When in doubt, ask questions! If we use a word that’s unfamiliar, make us explain it. “I’m confused about…” is always a great question.

Come to office hours!

Academic Honesty: Academic integrity is an important component of intellectual life and I treat cases of academic dishonesty very seriously. You are expected to uphold the principles in the Student Integrity Contract, to read and abide by the College policies on intellectual honesty in the Student Handbook, and to abide by any specific policies I establish. You will receive these policies in writing. If you have any questions you should bring them to me; when in doubt err on the side of caution and avoid even the appearance of academic dishonesty. The minimum penalty for academic dishonesty is a 0 on the given assignment. All cases of academic dishonesty will be referred to the Academic Honor Council.

 

Syllabus (207)

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Math 207, Spring 2016          

SYLLABUS

Instructor:                  Eli Goldwyn
Office Location:         MECC 265
Office Hours:            click “HOME” link above
Email:                          eli.goldwyn@trincoll.edu (please include “MATH 207” in the subject line!!!)

Class Meeting Time:    TR 9:25-10:40           room: McCook 303

Textbooks:

  • Statistics 13th ed. by McClave and Sincich, with MyStatmcclaveLab online course.
    • Instructions for creating MyStatLab account (if you don’t use the book store you may need to purchase MyStatLab separately).
    • If you are having trouble with MyStatLab check your browser settings, cookie and pop-up windows need to be enabled.
  • Investigating Statistical Concept, Applications, and Methods, by Beth Chance and Allan Rossman. Click here to purchase the $5 pdf version  (with both R and Minitab).

Weekly TA Sessions:

  • TBA

Course Description: An introductory course in statistics emphasizing modern techniques of data analysis: exploratory data analysis and graphical methods; random variables; probability distribution;  hypothesis testing, and confidence intervals; introduction to linear regression and least squares error.

Click here for a TED talk by Prof. Arthur Benjamin about why non-mathematician/engineers/scientists/economists should learn statistics instead of calculus (I took a class from Prof. Benjamin when I was an undergraduate)

Grading:

  • Attendance/Participation                                                    5%
  • Investigations                                                                         5%
  • HW (paper HW and online HW)                                        20%
  • Tests (2 midterms) (3/2, 4/18)                               20% each (40%)
  • Final Exam (cumulative) (5/10- 9:00 am)                       30%

Homework:

  • Paper HW will be graded on both the mathematical/statistical content and on the exposition, where appropriate (the correct answer may not be enough). I encourage you to work together, but you must submit your own work. These problems will be posted on the course website and will be turned in before class If your HW is multiple pages, staple pages together. If you use spiral notebook paper, remove fringes (you will lose points if you fail to do this — I know it’s annoying but otherwise grading the HW becomes impossible)!
  • StatLab-online HW uses the online program StatLab. Work is submitted through this program and is due by midnight on the due date.
  • Note: While all HW can be done open book/notes/internet and with classmates, if you need any of those resources to complete a problem, then you don’t really understand it. Be sure to practice some problems without any assistance- as if they are exam problems.

Exams: There will be two regular exams and a final exam. Make up exams are given only in the case of a serious medical problem or emergency documented by the Dean of Students office. Written documentation any such situation will be required. Advanced notice must be given if possible.

  • Exam Regrade Policy – If you think your exam was misgraded (I mis-added your points, I marked you wrong when your answer was correct, or you think you deserve more partial credit), you can return your exam to me with a letter (less than 1 page – can be handwritten neatly or printed out and signed in pen) describing why you deserve more points. You have one week from after I return the exams to submit this letter to me. Be sure to make this letter convincing.  Note: you can only do this one time per exam, so make sure you go through your entire exam BEFORE completing the above process.

Investigations: The investigations are found in the $5 pdf by Chance and Rossman.

  • Investigations will be worked on during class (see class schedule) in groups of 2-3 students.
    • Each group needs to bring at least 1 laptop/tablet and at least 1 printed out copy of the investigation.
  • Each group will turn in 1 copy of their completed Investigation
  • Investigations are due by the following class (though you will likely finish the Investigation during class and can turn it in right then).

Specific Classroom Rules:

  • You are expected to arrive for class on time and prepared, having completed any required reading and/or homework.
  • For the days where we are doing the investigations, I expect you to:
    • Read the introductory paragraph about that investigation before class starts
    • Find a group (2-3 students) where at least one person has a laptop/tablet, and at least one person has a printed off copy of the investigation
  • Cell phone use is for emergencies only! Please make sure the ringer is off!

Study Hints:

  • Come to class (and ask questions if you don’t understand).
  • Read the book BEFORE class.
  • Help each other (explaining a concept is a great way to understand it).
  • Attend my office hours and/or TA sessions, and visit the Q-center.
  • Review your class notes (I recommend doing this the same day).
  • Practice some HW or examples w/o friends or the book
  • Be patient! It’s okay if you don’t understand a concept the first time you see it.
  • VOX.com tips for “studying smarter”
  • The rule of thumb is ~2 hours of work outside of class for every hour of class

 

You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

  • Click here for a cool TEDx video (“Being a fantastic educator: a lesson from my niece”) about teaching that generally sums up my teaching philosophy (by coincidence the speaker is my college roommate’s younger brother).

Class Outline

  • Chapter 1: Intro to Statistics and Statistical Thinking
  • Chapter 2: Methods & Figures for Describing Sets of Data
  • Chapter 3: Probability
  • Chapter 4: Discrete Random Variables
  • Chapter 5: Continuous Random Variables
  • Chapter 6: Sampling Distributions
  • Chapter 7: Statistical Inference-Confidence Intervals
  • Chapter 8: Statistical Inference-Hypothesis Testing
  • Chapter 9: 2-population Statistical Inference  (skip)
  • Chapter 10: Analysis of Variance (skip)
  • Chapter 11: Linear Regression

Students with Academic Accommodations: Trinity College complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act.  If you have a documented disability and require academic accommodations, please present your accommodations letter during my office hours within the first two weeks of the semester. If you do not have a letter, but have questions about applying for academic accommodations, please contact Lori Clapis, Coordinator of Accommodation Resources, at 860-297-4025 or Lori.Clapis@trincoll.edu.

Academic Honesty: Academic integrity is an important component of intellectual life and I treat cases of academic dishonesty very seriously. You are expected to uphold the principles in the Student Integrity Contract, to read and abide by the College policies on intellectual honesty in the Student Handbook, and to abide by any specific policies I establish. You will receive these policies in writing. If you have any questions you should bring them to me; when in doubt err on the side of caution and avoid even the appearance of academic dishonesty. The minimum penalty for academic dishonesty is a 0 on the given assignment. All cases of academic dishonesty will be referred to the Academic Honor Council.

 

 

Syllabus (309)

By

Instructor: Eli Goldwyn
Course: Numerical Analysis (Math 309)
Office Location: MECC 265
Email: eli.goldwyn@trincoll.edu
Webpage: http://commons.trincoll.edu/egoldwyn/   (then click on Math 309)

Class Meeting Time: TR 10:50-12:05 (Clement – 308)

Office Hours: see main webpage (or by appointment)

Textbook: Numerical Analysis by Timothy Sauer, 2nd Ed. (available at the bookstore or online at amazon.com etc.)sauer_book
We will cover chapters 1-6 + additional section

Prerequisites: Computer Science 115, either MATH 132 or MATH 142, and any mathematics course numbered 200 or higher. Programming experience is recommended. See me if you have any questions.

 

Course Description: Theory, development, and evaluation of algorithms for mathematical problem solving by computation. Topics will be chosen from the following: interpolation, function approximation, numerical integration and differentiation, numerical solution of nonlinear equations, systems of linear equations, and differential equations. Treatment of each topic will involve error analysis.

Programming: All programming will be done in MATLAB unless you get permission from me. If you prefer to use a different programming language please discuss this with me immediately (before you begin any assignments).

MATLAB: All students should have access to MATLAB in the computer lab and/or on a personal computer.

Book MatLab programs:  link

Grading:
• Attendance/Class Participation/Quizzes 10%
• HW (theoretical HW and computational HW) 30%
• 2 Midterm Exams (dates: TBA) 30% (15% each)
• Final Exam (cumulative) 30% (take home 25%, in class 5%)

Homework:
• Will be posted weekly(ish) on the course website.
• HW will involve both theoretical and computational/programming exercises.
• Late HW will be penalized.
• Theoretical HW can be written up (cleanly) in pencil.
• Computational/programming HW should be using LaTex, Word, or some other program.
• HW will be posted on the webpage and will be due in my office Friday before 2:00 PM
• HW problems are the minimal amount of problems you should do. I recommend you do many more problems on your own!

Exams: There will be two regular exams and a final exam. Make up exams are given only in the case of a serious medical problem or emergency documented by the Dean of Students office. Written documentation any such situation will be required. Advanced notice must be given if possible.

Study Hints:
• Attend class and be active! (ask questions if you don’t understand).
• Read the book.
• Help each other/work in groups.
• Attend my office hours.
• Review your notes.
• Be patient! It’s okay if you don’t understand a concept the first time you see it.

A common theme emerges from this list: You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

Academic Honesty: Academic integrity is an important component of intellectual life and I treat cases of academic dishonesty very seriously. You are expected to uphold the principles in the Student Integrity Contract, to read and abide by the College policies on intellectual honesty in the Student Handbook, and to abide by any specific policies I establish. You will receive these policies in writing. If you have any questions you should bring them to me; when in doubt err on the side of caution and avoid even the appearance of academic dishonesty. The minimum penalty for academic dishonesty is a 0 on the given assignment/exam. All cases of academic dishonesty will be referred to the Academic Honor Council.

Coding and Academic Honesty: My general rule is you are encouraged to talk with others about general coding approaches and what they think of the results. All explanation/interpretations you write up should be your own. When it comes to debugging, half of learning and internalizing a programming language comes from finding and correcting your own mistakes. If you do get stumped and you need help debugging, try to only go as far as asking your classmate if they see what line the bug may be on. That way you still get a chance to think of the solution to problem yourself.
• You should never copy lines of code verbatim.
• You should never directly edit a fellow student’s .m file.
• You should never copy and paste.

 

CURRICULUM VITAE

By

PhD, University of California,Davis. (2008)

MS, New York University, Courant Institute. (2003)

BA, Pomona College.

TEACHING AWARDS

Winner 2013 ASUCD Excellence in Education Award for the College of Arts and Sciences (Division of Math and Physical Sciences)
Nominated for 2013 UC Davis Academic Federation Award for Excellence in Teaching

CV

RESEARCH

By

The central goal of my research is to use mathematics to better understand and manage natural populations. The role of theory in this process is to help uncover the mechanisms driving these systems and therefore improve the effectiveness of various control strategies. My research combines the development of mechanistic models describing  spatio-temporal systems with statistical inference based on data. Systems I have applied these techniques to include: predator-prey oscillators, the spread of infectious disease, and the opioid-epidemic.

The left figure illustrates the canonical example of spatial synchrony: the dynamics created by the predator-prey interactions of the lynx and the snowshare hare in Canada. My dissertation research uses the Theory of Weakly Coupled Oscillators to investigates the cause(s) of this interspecific spatial synchrony, where the leading explanations are migration and extrinsic climatic events.

The middle figure is a photograph on the North American gypsy moth. The gypsy moth is an invasive forest defoliator that causes widespread agriculture and forest damage. Aided by field data gathered by the Dwyer Lab, I am developing and fitting mechanistic models describing the interactions between the gyspy moth and its two primary pathogens, a density dependent NPV virus and a weather dependent fungus E. Maimaiga.

The figure on the right describes the number of reported cases of pertussis (also known as whooping cough) in the United States. While there are several leading hypothesis as to why there is this modern resurgence in incidence despite continued high vaccination rates, there is as yet no consensus. I am focused on trying to understand the role of spatial coupling in driving the interesting spatial patterns observed in the data.

Student Research:

SURE 2023

During the academic year 2018-2019, I was awarded a mini-grant from the Center for Undergraduate Research in Mathematics (CURM), to lead a group of five undergraduates researching the Opioid Epidemic. Our group consisted of UP students: Bryce Amato, Meghan Childs, Ruth Olson, Samantha Rivas, and Alexandra Tessner. Together, this group built an SIR-type compartmental model describing the relative roles of the four most commonly prescribed opioids on the size of this epidemic. They also used performed regression to examine the relationship between prescription rates and overdose death and the counter-intuitive recent inverse relationship between those two. They presented this work with talks at Founder’s Day at UP, the Spring 2019 MAA regional meeting, and at the Regional Annual meeting of AAAS. Sam and Alex continued this research with an independent study during academic year 2019-2020, they added to the model by approximating the addiction risk and prescription rates of each of the four most commonly prescribed opioids and performing sensitivity analyses on the size of the opioid epidemic with respect to each prescription rate. They found that oxycodone and codeine prescriptions played a larger roll than hydrocodone prescriptions. A manuscript based on these results has been published in Mathematical Medicine and Biology: A Journal of the IMA (link)

Subekshya Bidari created several stochastic SIR-type models describing three separate outbreaks of influenza that occurred at Trinity College in image1the spring of 2014 and 2016. Using data from the Trinity College Health Center on student influenza incidence and vaccination rates, Subekshya fit her models to this data using maximum likelihood techniques. More recent iterations of these models include different assumptions about the social networks of students and how that impacts disease transmission. Finally, we evaluated the  Subekshya has presented this research with talks at MathFest (2015 and 2016) and a poster presentation at the MBI organized Undergraduate Capstone Conference. This work has been published in the journal Letters in Biomathematics (link)

Kevin Liu and Shufan Wang completed an independent study with me on Convolutional Neural Networks for Visual Recognition. We followed an existing Stanford Class with of the same name (link). Using an existing library of photographs (CIFAR-10) as our training data, Kevin and Shufan created a convolutional neural network to identify additional (new) photographs. Network properties included a batch normalization layer, dropout, a pooling layer, and some preprocessing. As a “thank you project”, they created below images. Using neural style transfer, they passed an image of me (left) and allowed the image of me to adapt to the style of two famous paintings (Starry Night – middle, The Great Wave of Kanagawa – right)

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Rachel Lee wrote her senior thesis on a reaction-diffusion PDE model dScreen Shot 2016-11-15 at 10.03.34 PMescribing the growth and repair of long bones. Rachel non-dimensionalized  and simulated this model using the Crank-Nicholson numerical method. She found the parameter region that leads to the Turing Mechanism that mimics the concentration of two proteins critical in the biology of bone growth and repair.

IMG_1238Kalyan Parajuli created a novel adaptive time-step differential equation solver for a predator-prey oscillator. Kalyan calculated the phase response curve (the sensitivity of an oscillator’s phase to an external perturbation) and then built the solver to minimize the error after trying different relationships between the phase response curve and the time-step of the method. Kalyan presented his research with a poster at the Trinity College Annual Science Symposium.

Yaoqi Guo File_002studied the effectiveness of the Math Placement exam administered at Trinity using data from the last six years of students’ exam scores, high school GPA, SAT scores, and grade outcomes. Yaoqui looked at relationships between placement exams scores and outcome using chi-squared distribution, multiple regression analysis, student t-tests, and summary statistics. Yaoqui presented his research with a poster at the Trinity College Annual Science Symposium.

Pranav Bhandari compared the numerical error between a variety of different numerical methods approximating solutions to the Lotka-Volterra predator-prey model. Pranav looked at fixed time step methods of different orders, two-step methods, implicit methods, and adaptive-time step methods and compared the error propagated in each method with the computational complexity of the method. Pranav presented his research with a poster at the Trinity College Annual Science Symposium.