Abstract data types including priority queues and dynamic dictionaries and efficient data structures for these data types, including heaps, self-balancing trees, and hash tables. Analysis of data structures including worst-case, average-case and amortized analysis. Storage allocation and reclamation. Secondary storage considerations. Extensive practice building programs for a variety of applications.

Algorithm design, analysis, and correctness. Design techniques including divide-and-conquer and dynamic programming. Analysis techniques including solutions to recurrence relations and amortization. Correctness techniques including invariants and inductive proofs. Applications including sorting and searching, graph theoretic problems such as shortest path and network flow, and topics selected from arithmetic circuits, parallel algorithms, computational geometry, and others. An introduction to computational complexity, NP-completeness, and approximation algorithms. Proficiency with programming is expected as some assignments require algorithm implementation.

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.

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.

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.

An introduction to electricity and magnetism leading to Maxwell’s elec­tromagnetic equations in differential and integral form. Selected topics in classical and quantum optics.

The development and formulation of quantum mechanics, and the application of quantum mechanics to topics in atomic, solid state, nuclear, and particle physics.

Classical experiments of modern physics, including thermal radiation and Rutherford scattering. Nuclear physics experiments, including alpha, beta and gamma absorption, and gamma spectra by pulse height analysis. Analysis of the buildup and decay of radioactive nuclei.

This course combines mathematical and computational methods that are useful for studying physical systems. Topics include: Linear algebra, Hilbert spaces, the eigenvalue problem and numerical algorithms for solving problems in linear algebra, including various modes of decomposition; Fourier series and transforms, convolution, correlation and numerical methods using fast Fourier transforms; computer simulation methods based on integrating coupled differential equations and also using pseudorandom numbers, including Monte Carlo methods; partial differential equations, separation of variables, Laplace and Poisson equations in various dimensions, the wave equation, and numerical approaches to solution.

The application of mathematical methods to the study of particles and of systems of particles; Newton, Lagrange, and Hamilton equations of motion; conservation theorems; central force motion, collisions, damped oscillators, rigid body dynamics, systems with constraints, variational methods.

Classical and quantum statistical mechanics, including their connection with thermodynamics. Kinetic theory of gases. Applications of these concepts to various physical systems.

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.