biology

Mathematical Biology

Mathematical Biology is a biology topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mathematical Biology rather than just read about it. In short: Mathematical Biology is a two-part monograph on mathematical biology first published in 1989 by the applied mathematician James D. Murray.

Key takeaways

Mathematical Biology belongs to biology; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mathematical Biology to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mathematical Biology from memory before moving on to harder problems.

Reference excerpt

Mathematical Biology is a two-part monograph on mathematical biology first published in 1989 by the applied mathematician James D. Murray. It is considered to be a classic in the field and sweeping in scope.

Part I: An Introduction Part I of Mathematical Biology covers population dynamics, reaction kinetics, oscillating reactions, and reaction-diffusion equations.

Chapter 1: Continuous Population Models for Single Species Chapter 2: Discrete Population Models for a Single Species Chapter 3: Models for Interacting Populations Chapter 4: Temperature-Dependent Sex Determination (TSD) Chapter 5: Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair Chapter 6: Reaction Kinetics Chapter 7: Biological Oscillators and Switches Chapter 8: BZ Oscillating Reactions Chapter 9: Perturbed and Coupled Oscillators and Black Holes Chapter 10: Dynamics of Infectious Diseases Chapter 11: Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms Chapter 12: Oscillator-Generated Wave Phenomena Chapter 13: Biological Waves: Single-Species Models Chapter 14: Use and Abuse of Fractals

Part II: Spatial Models and Biomedical Applications Part II of Mathematical Biology focuses on pattern formation and applications of reaction-diffusion equations. Topics include: predator-prey interactions, chemotaxis, wound healing, epidemic models, and morphogenesis.

Chapter 1: Multi-Species Waves and Practical Applications Chapter 2: Spatial Pattern Formation with Reaction Diffusion Systems Chapter 3: Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms Chapter 4: Pattern Formation on Growing Domains: Alligators and Snakes Chapter 5: Bacterial Patterns and Chemotaxis Chapter 6: Mechanical Theory for Generating Pattern and Form in Development Chapter 7: Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies Chapter 8: A Mechanical Theory of Vascular Network Formation Chapter 9: Epidermal Wound Healing Chapter 10: Dermal Wound Healing Chapter 11: Growth and Control of Brain Tumours Chapter 12: Neural Models of Pattern Formation Chapter 13: Geographic Spread and Control of Epidemics Chapter 14: Wolf Territoriality, Wolf-Deer Interaction and Survival

Impact Since its initial publication, the monograph has come to be seen as a highly influential work in the field of mathematical biology. It serves as the essential text for most high level mathematical biology courses around the world, and is credited with transforming the field from a niche subject into a standard research area of applied mathematics.

References

External links Mathematical Biology I: An Introduction Mathematical Biology II: Spatial Models and Biomedical Applications

Worked examples

Example 1 — a first encounter with Mathematical Biology

Start with the simplest possible case. Write down what Mathematical Biology claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mathematical Biology before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mathematical Biology ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mathematical Biology

In research: Mathematical Biology appears in biology research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mathematical Biology in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mathematical Biology is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biology books, Mathematical and theoretical biology, so understanding it makes those chapters shorter.
In everyday life: Look for Mathematical Biology outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mathematical Biology in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mathematical Biology means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mathematical Biology out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mathematical Biology in simple terms?

Mathematical Biology is a two-part monograph on mathematical biology first published in 1989 by the applied mathematician James D. Murray.

Why does Mathematical Biology matter?

Because it connects several biology ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mathematical Biology?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mathematical Biology.