Bio Maths Course

Lesson 1 • Graphing and Data Visualization Basics

Introduces coordinate systems, graph types, and slope interpretation for biological data. Prepares students to read and construct scientific graphs accurately.

Lesson 2 • Algebraic Reasoning for Biological Problems

Applies linear and quadratic algebra to biological scenarios such as dosage and concentration. Connects symbolic manipulation to real biological quantities.

Lesson 3 • Ratios, Proportions, and Scaling

Examines ratios and scaling laws that govern organism size and physiological rates. Provides tools for comparing biological quantities across scales.

Lesson 1 • Frequency Distributions and Histograms

Constructs frequency tables and histograms from raw biological measurements. Reveals distributional shape relevant to population and ecological studies.

Lesson 2 • Measures of Variability and Spread

Covers variance, standard deviation, and range to quantify biological variability. Links spread measures to biological diversity and experimental reproducibility.

Lesson 3 • Sampling and Data Collection Principles

Explains random sampling, sample size, and bias in biological field and lab studies. Grounds statistical inference in sound data collection practice.

Lesson 4 • Correlation and Covariance in Biology

Quantifies linear relationships between biological variables using covariance and Pearson correlation. Distinguishes correlation from causation in biological contexts.

Lesson 1 • Discrete Probability Distributions

Covers binomial and Poisson distributions with applications to mutation rates and rare events. Connects distribution choice to biological data-generating processes.

Lesson 2 • Continuous Probability Distributions

Introduces normal and exponential distributions for modeling biological measurements and survival. Links distribution properties to biological phenomena such as trait variation.

Lesson 3 • Conditional Probability and Independence

Applies conditional probability and Bayes' theorem to diagnostic testing and genetic inheritance. Clarifies independence assumptions critical in biological modeling.

Lesson 4 • Probability in Genetic Inheritance

Uses probability rules to predict genotype and phenotype ratios in Mendelian and non-Mendelian crosses. Reinforces probability concepts through Punnett squares and chi-square tests.

Lesson 1 • Linear and Polynomial Functions in Biology

Models biological relationships with linear and polynomial functions, including calibration curves. Provides the simplest functional forms before introducing nonlinear models.

Lesson 2 • Logistic Growth and Carrying Capacity

Models population growth with the logistic equation incorporating carrying capacity limits. Extends exponential models to realistic resource-constrained biological systems.

Lesson 3 • Enzyme Kinetics and Saturation Models

Derives and applies the Michaelis-Menten equation to describe enzyme reaction rates. Connects hyperbolic saturation curves to biochemical substrate-enzyme interactions.

Lesson 4 • Exponential and Logarithmic Functions

Applies exponential growth and decay models to population dynamics and radioactive tracers. Introduces logarithms as tools for linearizing biological data.

Lesson 1 • Differentiation and Biological Rates

Derives derivatives of biological functions to compute instantaneous growth and reaction rates. Applies chain and product rules to composite biological models.

Lesson 2 • Limits and Continuity in Biological Contexts

Introduces limits and continuity as foundations for understanding instantaneous biological rates. Connects asymptotic behavior to saturation phenomena in biology.

Lesson 3 • Ordinary Differential Equations in Biology

Formulates and solves first-order ODEs for population growth, decay, and pharmacokinetics. Establishes ODE modeling as the core language of dynamic biological systems.

Lesson 4 • Partial Derivatives and Multivariable Biology

Extends differentiation to functions of multiple biological variables such as fitness landscapes. Prepares students for multivariable optimization in ecological and evolutionary models.

Lesson 1 • Hypothesis Testing Framework

Establishes null and alternative hypotheses, significance levels, and decision rules for biological tests. Distinguishes Type I and Type II errors in experimental biology.

Lesson 2 • Parametric Tests for Biological Data

Applies t-tests and ANOVA to compare means across biological treatment groups. Verifies assumptions of normality and homogeneity of variance before testing.

Lesson 3 • Nonparametric and Chi-Square Tests

Uses rank-based and chi-square tests when biological data violate parametric assumptions. Applies goodness-of-fit and independence tests to categorical biological data.

Lesson 4 • Sampling Distributions and the Central Limit Theorem

Explains how sample means distribute and why the central limit theorem enables inference. Grounds confidence interval and hypothesis test logic in sampling theory.

Lesson 1 • Principles of Mathematical Model Building

Defines model types, assumptions, and the iterative modeling cycle in biological science. Establishes criteria for model adequacy, parsimony, and biological realism.

Lesson 2 • Compartmental Models in Biology

Develops SIR and pharmacokinetic compartmental models using systems of ODEs. Applies compartmental thinking to disease spread and drug distribution dynamics.

Lesson 3 • Predator-Prey and Competition Models

Analyzes Lotka-Volterra equations for predator-prey and interspecific competition dynamics. Identifies equilibria and stability to predict long-term ecological outcomes.

Lesson 4 • Stochastic Models and Biological Randomness

Introduces stochastic processes including birth-death models and random walks in biology. Contrasts stochastic outcomes with deterministic predictions for small populations.

Lesson 1 • Optimization in Biological Systems

Applies constrained and unconstrained optimization to evolutionary fitness and resource allocation. Uses Lagrange multipliers and linear programming in biological optimization problems.

Lesson 2 • Network Theory in Biological Systems

Models food webs, gene regulatory networks, and neural circuits as mathematical graphs. Quantifies connectivity, centrality, and robustness of biological networks.

Lesson 3 • Regression Modeling for Biological Data

Extends simple regression to multiple and logistic regression for complex biological datasets. Evaluates model fit, multicollinearity, and predictor significance in biological contexts.

Lesson 4 • Matrix Algebra and Population Projection

Uses matrix multiplication and eigenanalysis to project structured population dynamics over time. Connects Leslie matrix outputs to conservation and management decisions.