Course Descriptions

Analytical Methods in Biology (694:230)

This course may also be used to fulfill the elective requirements of the Biological Sciences and MBB majors.


Offered:  Spring  T/H4 (Tues/Thurs 5:40 - 7:00 PM) Tillet 207 Livingston  

Credits:  3

Prerequisites:  General Biology (01:119:116)  and  Calculus I (01:640:135 or 01:640:151)

Overview of Course:

This course is for students interested in learning numerical techniques for biology applications.  Matlab will be used as a programming tool. All the methods and ideas presented will be developed using concrete examples of how they apply to actual biological phenomena. 

Course Topics: 

  • Probability Theory, Theory of Distributions and Moments, Central Limit Theorem,
  • Linear and non-Linear Regression, 
  • Parametric and Non-Parametric Tests of Significance and Analysis of Variance (ANOVA).
  • Hardy Weinberg Theory, Mathematics of Mutations, Drift, Recombination and Selection. 
  • Sequence Alignment and Phylogenetic Analysis 
  • Clustering Methods: k-means clustering, Principle Component Analysis (PCA), t-SNE and non-negative matrix factorization. 
  • Analysis of high throughput RNA and DNA sequencing data 
  • Monte Carlo Simulations
  • Modeling the Covid-19 pandemic 
  • Neural Networks
  • Evolutionary Game Theory

Lecture notes will be distributed in advance of lectures and students are expected to have read these notes before class. For each topic, there will be one formal lecture and an in-class worksheet which we will work through in class. The students must complete the worksheet on their own after class and uploaded their solutions on Canvas by Sunday 11:59 PM of the week of the class. These worksheets will count for 30% of the grade. In addition, homework on the material covered will be posted on Canvas and will be due approximately one week later. Homework will also count for 30% of the grade. There will be two mid-terms (15% of grade each) but no final.  Students will be required to read a book they choose from a list provided by the instructor and will present a formal summary of this book in class at the end of the semester. This will count for 10% of the grade. 

Course Schedule: 

Week 1-4

  • Introduction to the class and Matlab Tutorial
  • Introduction to Probability Theory, Bayes Theorem, Random Variables; Expected Value and Variance.
  • Distribution Theory - Binomial, Poisson, Bernoulli & Geometric Distributions
  • Demonstration of Central Limit Theorem.
  • Parametric Tests of Significance based on the Central Limit Theorem (t-test, F-test, ANOVA)
  • Non-parametric tests of significance

Week 5-9

  • Bio Intro, The Genetic Code, Mutation and Drift, Hardy Weinberg Theory
  • Analytical methods to understand Recombination and Selection.
  • Sequence Alignment and Phylogenetics.
  • Clustering Methods: k-means clustering, PCA, t-SNE and non-negative matrix factorization methods.
  • Mid-term and assignment of term paper topics after week 6.

Week 9-14

  • Analysis of Genetic and Genomic data using the techniques learned.
  • Introduction to Viruses - FLU, HIV, SARS, MERS and Zoonotic diseases
  • Analytical Modeling – The SIR Model of Pandemics - Modeling Covid-19 data
  • Monte Carlo Simulations
  • Neural Networks
  • Evolutionary Game Theory
  • Mid-Term 2
  • Class book presentations

Course URL: Canvas

Course satisfies Learning Goals

MBB Departmental Learning Goals: 1, 2,and 3

Course Learning Goals:  The overall goal of this course is to give the students the mathematical tools and programming skills necessary to analyze and interpret biological and biomedical data correctly and with confidence. 

Course Materials

Matlab: Students should download and install Matlab on their laptops and always bring your laptops with Matlab installed to class. To download and install Matlab, start from the following link: https://www.mathworks.com/academia/tah-portal/rutgers-university-354167.html

Course Closed?  Enrollment is limited to 50 students.

 Faculty:  Course Coordinator: This email address is being protected from spambots. You need JavaScript enabled to view it.  This email address is being protected from spambots. You need JavaScript enabled to view it. or gyanbhanot@gmail,com (preferred) NOTE: All your emails must originate from your net-id email because not having a net-id means you are not officially registered to take the course.  848-391-7508. Office hours: There will be two 1-hour long online office hours. The timing of these will be arranged by discussion in class with students.

Academic Integrity:

Students are expected to maintain the highest level of academic integrity.  You should be familiar with the university policy on academic integrity: http://academicintegrity.rutgers.edu/academic-integrity-policy/  Violations will be reported and enforced according to this policy.

Use of external sources to obtain solutions to homework assignments or exams is cheating and a violation of the University Academic Integrity policy. Cheating in the course may result in penalties ranging from a zero on an assignment to an F for the course, or expulsion from the University.  Posting of homework assignments, exams, recorded lectures, or other lecture materials to external sites without the permission of the instructor is a violation of copyright and constitutes a facilitation of dishonesty, which may result in the same penalties as explicit cheating.

Not only does the use of such sites violate the University’s policy on Academic Integrity, using such sites interferes with your achievement of the learning you are paying tuition for. Assignments, quizzes, and exams are given not simply to assign grades, but to promote the active learning that occurs through completing assignments on your own.  Getting the right answer is much less important than learning how to get the right answer.  This learning is critical to your success in subsequent courses and your careers.