A comprehensive view of the theory and techniques of differential and integral calculus of a single variable together with a robust introduction to multivariable calculus. Topics include limits, continuity, derivatives, definite integrals, infinite series, Taylor series in one and several variables, partial derivatives, double and triple integrals, linear approximations, the gradient, directional derivatives and the Jacobian, optimization and the second derivative test, higher-order derivatives and Taylor approximations, line integrals, vector fields, curl, divergence, Green’s theorem, and an introduction to flux and surface integrals.

Topics include combinatorics (clever ways of counting things), number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs. Possible applications include probability, analysis of algorithms, and cryptography.

Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization. General vector spaces and linear transformations; change of basis and similarity. Additional Topics.

Modeling physical systems, first-order ordinary differential equations, existence, uniqueness, and long-term behavior of solutions; bifurcations; approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability. Additional topics.

The goal of this course is to improve students’ ability to communicate mathematics, both to a general and technical audience. Students will present material on assigned topics and have their presentations evaluated by students and faculty. This format simultaneously exposes students to a broad range of topics from modern and classical mathematics. Required for all majors; recommended for all joint CS-math majors and mathematical biology majors, typically in the junior year.

An introduction to the concepts of modern engineering, emphasizing modeling, analysis, synthesis, and design. Applications to chemical, mechanical, and electrical systems. A course materials fee, payable to the HMC Department of Engineering, applies. No textbook purchase required.

Application of molecular biology techniques to problems in human genetics, bioengineering, and environmental sensing.

Topics in ecology, evolution, molecular genetics, and computational biology.

Investigations in physiology, biochemistry, ecology, molecular biology, and other areas of experimental biology.

An introduction to the field of mathematical biology. Continuous and discrete mathematical models of biological processes and their analytical and computational solutions. Examples may include models in epidemiology, ecology, cancer biology, systems biology, molecular evolution, and phylogenetics.

An introduction to the field of computational biology. Algorithms for phylogenetic inference and computational methods for solving problems in molecular evolution and population genetics.

Statistical techniques for analyzing biological data, including parametric, nonparametric, and randomization methods. Statistical aspects of experimental design with an emphasis on analyzing data collected in BIOL 054.

Students registered for joint colloquium must attend a fixed number of colloquium talks during the semester in any field(s) related to their interests. The talks may be at any members of The Claremont Colleges or a nearby university and may be in any of a wide array of fields including biology, mathematics, computer science and other science and engineering disciplines including bioengineering, cognitive science, neuroscience, biophysics, and linguistics. Students enrolled in the joint colloquium are required to submit a short synopsis of each talk that they attend. No more than 2.0 credits can be earned for departmental seminars/col­loquia.

Applications of thermodynamics, equilibria, electrochemistry, structure/property relationships, synthesis and spectroscopy.

Chemistry plays a powerful role in addressing an array of current and future global and societal challenges. This course examines contemporary applications of chemistry to describe innovative advances in such areas as energy, medicine, technology, materials, to name a few. These applications illustrate such fundamental concepts as molecular and electronic structure in dictating chemical and physical properties; intermolecular forces, phase behavior, thermodynamics, electrochemistry, kinetics, and equilibria. Lecture and individual and group exercises conducted in class are used as a context for introducing chemistry principles.

Einstein’s special theory of relativity is developed from the premises that the laws of physics are the same in all inertial frames and that the speed of light is a constant. The relationship between mass and energy is explored and relativistic collisions analyzed. The families of elementary particles are described and the equivalence principle developed.

Classical mechanics is introduced beginning with inertial frames and the Galilean transformation, followed by momentum and momentum conservation in collisions, Newton’s laws of motion, spring forces, gravitational forces and friction. Differential and integral calculus are used extensively throughout. Work, kinetic energy and potential energy are defined, and energy conservation is discussed in particle motion and collisions. Rotational motion is treated, including angular momentum, torque, cross-products and statics. Other topics include rotating frames, pseudoforces and central-force motion. Simple harmonic and some nonlinear oscillations are discussed, followed by waves on strings, sound and other types of waves, and wave phenomena such as standing waves, beats, two-slit interference, resonance and the Doppler effect.

This course emphasizes the evidence-based approach to understanding the physical world through hands-on experience, experimental design, and data analysis. Experiments are drawn from a broad range of physics subjects, with applications relevant to modern society and technology.

In this course our focus is to prepare Harvey Mudd students for the lifelong challenge of fostering “a clear understanding of the impact of their work on society.” We will use climate change as an opportunity to explore the impact of our work on society. There are four primary components of that exploration: critical analysis of the social context of STEM, the expansion and application of concepts from the core to understand this social-technical problem, collaborative projects that promote positive change in the world, and communicating our project designs and professional choices. Plenary sessions will explore topics such as environmental justice, earth system science, the relation between expertise and power, policy processes, data science, community engagement, multidisciplinary collaboration, impactful careers, and science communication. Individual sections will explore particular climate-related issues in greater depth. Final team projects will challenge students to apply these concepts in proposals for climate solutions.