Vardayani Ratti




My research interest is in Mathematical Biology, in particular applications in ecology, infectious diseases, pollination biology and agriculture.
I am looking for undergraduate or graduate students who want to pursue research in this area. If you are interested, please email me.


Recent invited talks


  • California State University, Chico, USA, 2019

  • Rochester Institute of Technology, Rochester, USA, 2018

  • Arizona State University, Arizona, USA, 2018

  • AMS Special Session at Spring Eastern Sectional Meeting, Northeastern University, Boston, 2018

  • Sonia Kovalevsky Day, Dartmouth College, USA, 2018

  • Bowdoin College, Maine, USA, 2018

  • Fields Institute's Workshop on Pollinators and Pollination Modeling, Toronto, 2018

  • Joint Mathematics Meeting, San Diego, USA, 2018

  • Minisymposium on Mathematical Biology, Dartmouth College, 2017

  • Joint Mathematics Meetings, Atlanta, USA, 2017

Contact

Assistant Professor
California State University, Chico
Department of Mathematics and Statistics
400 W 1st St
Chico, CA 95929
Email: vratti@csuchico.edu
Phone: (+1) 530-898-5508
Office: 136 Holt Hall
Zoom Office:Meeting ID: 747 064 4517, Passcode: 271556


Research


Publications (undergraduate co-authors are in bold)




Under revision (undergraduate co-authors are in bold)



In preparation (undergraduate co-authors are in bold)


  • Wallace, D.I.; Kachalia, A.A.; Ratti, V. Effect of habitat diversity on the population dynamics of Anopheles gambiae.

  • A mathematical model of beevectoring applied to the biocontrol of Botrytis cineria by clonostachys rosea f. rosea)
  • A review of the mathematical models in honeybee colonies

Book Chapter



Theses


  • Ratti, V. Predictive Modeling of the Disease Dynamics of Honeybee-Varroa destructor-Virus Systems. Ph.D. Thesis

  • Ratti, V. Local Stability Analysis of the Honeybee-Varroa destructor-Acute Bee Paralysis Virus. M.Sc. Thesis

Teaching



Fall 2020, Spring 2020


MATH 217: Discrete Mathematics

(Blackboard, student access only)

A rigorous introduction to discrete mathematical structures for computer science majors (fulfills a requirement for the minor in math). Topics include propositional and predicate calculus; basic proof methods; sets, functions, and operations with them; algorithms and their complexity; applications of number theory to computer science and computer security; matrices and matrix arithmetic; mathematical induction, recursive definitions and algorithms; combinatorics and counting techniques; relations and their representation by matrices and digraphs, applications to databases; equivalence relations and partitions of sets; partially ordered sets, lattices, and Boolean algebras; Boolean functions and circuits; graphs, trees, and their applications; formal languages and grammars; finite-state automata and language recognition, regular languages.


Textbook: Applied Discrete Structures by Al Doerr & Ken Levasseur, 2019


MATH 120: Analytic Geometry and Calculus

(Blackboard, student access only)

Limits and continuity. The derivative and applications to related rates, maxma and minima, and curve sketching. Transcendental functions. An introduction to the definite integral and area.


Textbook: Stewart’s Calculus 8E Early Transcendentals, published by Cengage.


Previous courses


MATH 3: Calculus

(Winter and Fall 2018)

This course involves collaborative learning. It is an introduction to single variable calculus aimed at students who have seen some calculus before, either before matriculation or in introductory calculus course (Math 1). Math 3 begins by revisiting the core topics in Math 1 - convergence, limits, and derivatives - in greater depth before moving to applications of differentiation such as related rates, finding extreme values, and optimization. The course then turns to integration theory, introducing the integral via Riemann sums, the fundamental theorem of calculus, and basic techniques of integration.


Textbook: ``Calculus'' by Herman and Strang's, Volume 1. (open access PDF)


Math 8: Calculus of Functions of one and Several Variables

(Spring 2018)

This course is a sequel to Math 3 and provides an introduction to Taylor series and functions of several variables. The first third of the course is devoted to approximation of functions by Taylor polynomials and representing functions by Taylor series. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables.


Textbook: ``Calculus", by James Stewart, 8th Edition, ISBN: 978-1-285-74062-1

MATH 76: Topics in Applied Mathematics

(Winter 2018)

This course is designed to provide students with the basic tools for building and analyzing mathematical models in Biology primarily using ordinary differential equations. In addition, you will learn how to analyze and simulate the models. You will also learn to interpret and communicate the results in the context of biology.


Textbooks:

MATH 22: Linear Algebra with Applications

(Fall 2017, Spring 2019)

This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.


Textbook: Linear Algebra and Its Applications (5th Edition) by David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson 2015


Math 13: Multivariable Calculus

(Winter 17)

This course is a sequel to Math 8 and provides an introduction to calculus of vector-valued functions. The course starts with iterated, double, triple, and surface integrals including change of coordinates. The remainder of the course is devoted to vector fields, line integrals, Green’s theorem, curl and divergence, and Stokes’ theorem.


Textbook: ``Calculus Early Transcendentals Multivariable", by Rogawski & Adams, 3rd Edition, ISBN: 978-1464171758



MATH 23: Differential Equations

(Fall 2016)

This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations using eigenvectors and eigenvalues, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series.


Textbook: Elementary Differential Equations and Boundary Value Problems (10th Edition) by Boyce & DiPrima, Wiley 2012

Graduate Teaching Assistant (2009 - 2015)