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An Invitation to Mathematical Biology

  • Textbook
  • © 2023

Overview

Authors:
  1. David G Costa

    1. Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Paul J Schulte

    1. School of Life Sciences, University of Nevada, Las Vegas, Las Vegas, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Designed to provide an introduction to the field of mathematical biology for students of all levels
  • Illustrates mathematical concepts using examples of biological systems
  • Demystifies computational biology for non-computer scientists

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About this book

The textbook is designed to provide a "non-intimidating" entry to the field of mathematical biology.  It is also useful for those wishing to teach an introductory course.  Although there are many good mathematical biology texts available, most books are too advanced mathematically for most biology majors.  Unlike undergraduate math majors, most biology major students possess a limited math background. Given that computational biology is a rapidly expanding field, more students should be encouraged to familiarize themselves with this powerful approach to understand complex biological phenomena. Ultimately, our goal with this undergraduate textbook is to provide an introduction to the interdisciplinary field of mathematical biology in a way that does not overly terrify an undergraduate biology major, thereby fostering a greater appreciation for the role of mathematics in biology

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • David G Costa, Paul J Schulte
    Pages 1-2

  3. Exponential Growth and Decay

    • David G Costa, Paul J Schulte
    Pages 3-10

  4. Discrete Time Models

    • David G Costa, Paul J Schulte
    Pages 11-14

  5. Fixed Points, Stability, and Cobwebbing

    • David G Costa, Paul J Schulte
    Pages 15-20

  6. Population Genetics Models

    • David G Costa, Paul J Schulte
    Pages 21-28

  7. Chaotic Systems

    • David G Costa, Paul J Schulte
    Pages 29-35

  8. Continuous Time Models

    • David G Costa, Paul J Schulte
    Pages 37-42

  9. Organism-Organism Interaction Models

    • David G Costa, Paul J Schulte
    Pages 43-49

  10. Host-Parasitoid Models

    • David G Costa, Paul J Schulte
    Pages 51-56

  11. Competition Models with Logistic Term

    • David G Costa, Paul J Schulte
    Pages 57-64

  12. Infectious Disease Models

    • David G Costa, Paul J Schulte
    Pages 65-71

  13. Organism Environment Interactions

    • David G Costa, Paul J Schulte
    Pages 73-82

  14. Back Matter

    Pages 83-124
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Reviews

“This very brief volume is designed for biology undergraduates with only a basic calculus background. … it is very self contained, with the appendixes providing the basics of standard numerical packages.” (Louis J. Gross, The Quarterly Review of Biology, Vol. 100 (1), March, 2025) 

“I think the authors have succeeded in their goal of providing an ‘invitation’ to mathematical biology. Not only can this book serve as a stepping stone to more comprehensive mathematical biology books, it also offers the reader a glimpse into a variety of topics that they can pursue in deeper detail later on if they are interested.” (Anita T. Layton, SIAM Review, Vol. 66 (3), August, 2024)

Authors and Affiliations

  • Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, USA

    David G Costa

  • School of Life Sciences, University of Nevada, Las Vegas, Las Vegas, USA

    Paul J Schulte

About the authors

David G Costa is a mathematician interested in Partial Differential Equations (PDEs), Ordinary Differential Equations (ODEs) and the Calculus of Variations. In particular, he is interested in the use of so-called variational and topological techniques to study qualitatively and visualization of phenomena in PDEs and ODEs. Such phenomena are present in various areas of sciences, including physics, biology, and chemistry, among others. He teaches a variety of courses at the undergraduate level (including Calculus, Linear Algebra, ODEs, PDEs, and Introductory Real Analysis), and graduate level (including PDEs, and Real Analysis), as well as a course in Biomathematics jointly offered by the Department of Mathematical Sciences and School of Life Sciences.


Paul J Schulte is a plant physiologist interested in biophysical approaches to studying internal processes in plants.  These commonly involve applications of mathematical approaches asrealized through computational solutions.  Plants are dependent on water for survival and their ability to acquire water from the soil and transport it throughout the plant is determined in part by the hydraulic properties of the plant's tissues.  Most of his work considers transport processes such as water flow in the xylem tissues or sugar flow in the phloem tissues.  He teaches a variety of courses such as Plant Physiology, Plant Anatomy, Introduction to Biological Modeling, and Biomathematics jointly offered in the School of Life Sciences and Department of Mathematical Sciences.



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