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# Biomathematics Research

### - Overview

Biomathematics, also known as mathematical and theoretical biology, is a branch of biology that uses mathematical models and abstractions to study the principles that govern biological systems.

Biomathematics can be used in both theoretical and practical research. It has been used in areas such as: Cellular neurobiology, Epidemic modeling, Population genetics.

Biomathematics can help develop analytical and predictive models of biological and medical systems. For example, mathematical modeling can help improve disease treatment and streamline biochemical processes.

Biomathematics can also help construct mathematical models that represent the complex interactions of biological systems. These models can help researchers understand and explore the consequences of these interactions.

Biomathematics researchers develop mathematical and statistical models and methods to study biological phenomena. For example, they may develop models of cancer or infectious diseases.

The term "biomathematics" was coined in 1923 by William Moses Feldman.

### - Mathematical Biology (or Biomathematics)

Mathematical biology is a broad topic that can cover a wide range of length scales, from the submicron lengths of DNA polymers to the kilometer length scales of animal migratory patterns.

Mathematical biology is a branch of biology that uses mathematical models and analysis to study the structure, development, and behavior of biological systems. It's also known as biomathematics or mathematical and theoretical biology.

Mathematical biology uses mathematical techniques and tools to model natural biological processes. It has both practical and theoretical applications in biological research.

Mathematical biology has led to the creation of new fields within mathematics, such as pattern formation in reaction-diffusion equations and combinatorial problems in sequence alignment.

Mathematical biology is rapidly expanding and developing as scientists in the biological sciences move from descriptive to more quantitative experiments. The diversity and complexity of living organisms means that mathematicians face additional challenges in interpreting and predicting biological systems through modeling.

### - Mathematical and Theoretical Biology

Biomathematics is an interdisciplinary field that combines biology and mathematics. Research in biology is usually based on experimentation with materials, while in mathematical biology experimentation is theoretical.

Mathematical and theoretical biology, or biomathematics, is that branch of biology that uses theoretical analysis, mathematical models, and abstractions of living organisms to study the principles governing the structure, development, and behavior of systems, as opposed to experimental biology, which deals with conducting Experiments to prove and verify scientific theories.

The field is sometimes called mathematical biology or biomathematics to emphasize the mathematical aspects, or theoretical biology to emphasize the biological aspects.

Theoretical biology focuses more on the development of biological theoretical principles, while mathematical biology focuses on the study of biological systems using mathematical tools, although the two terms are sometimes used interchangeably.

Mathematical biology aims at the mathematical representation and modeling of biological processes using techniques and tools of applied mathematics. It is useful in both theoretical and practical research.

Describing systems in a quantitative way means that their behavior can be better modeled, so properties that may not be apparent to the experimenter can be predicted. This requires precise mathematical models.

Due to the complexity of living systems, theoretical biology employs multiple fields of mathematics and contributes to the development of new technologies.

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### - Math Subjects of Biomathematics

Biomathematics is a broad field that uses mathematical models to understand biological phenomena. It involves all areas of mathematics, including:
• Real and complex analysis
• Integral and differential systems
• Metamathematics
• Algebra
• Geometry
• Number theory
• Topology
• Probability

Biomathematics also uses "esoteric math" like algebraic topology, category theory, and number theory.

Some examples of biological systems that have been studied in biomathematics include:

• The human genome
• Population level genetics
• Cancer cells
• Ecologically invasive species
• The immune system
• Regional and global epidemics

Some math subjects related to biomathematics include:

• Multivariable Calculus
• Linear Algebra
• Probability & Simulation
• Probability Theory
• Math Statistics
• Agent-Based Modeling
• Real Analysis

Biomathematics also involves basic programming, probability, and statistics.

### - Research Topics in Mathematical Biology

Mathematical biology is a field of research that uses mathematical models to represent biological systems. These models can help predict and describe natural occurrences and populations.

Some topics in mathematical biology include:

• Systems biology: Understanding complex life processes using molecular set theory, relational biology, and algebraic biology.
• Genomics: Accessing an organism's genome is similar to understanding a language's alphabet without knowing what words mean or how sentences are structured.
• Population dynamics: Understanding the basic relationships between species.
• Evolutionary biology: Studying the patterns of variation among entities and the processes that generate their diversity.

Other topics in mathematical biology include:

• Protein interactions and mobility
• Regulation of gene expression
• Cell behavior
• Tissue mechanics
• Immune responses
• Epidemic dynamics
• Bacterial cell division
• The evolution of cooperation
• Game theory
• Speciation
• Social aggregation (swarming)

[More to come ...]