ENGR 11a Introduction to Design Methodology
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Prerequisite: Instructor permission required.

An introduction to the engineering design process, with a focus on human-centered design. Students work in teams to solve authentic design problems under the theme of “design to repair the world.” Students are guided through a highly scaffolded process in which they form an idea, sketch it, and develop it through multiple iterations leveraging quick feedback loops and the Design Thinking methodology. Students will become fluent in basic additive and subtractive manufacturing, including 3D printing, laser cutting, and CNC machining. Usually offered every year.

ENGR 12b Engineering Instrumentation and Experimentation
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Prerequisites: MATH 10a and PHYS 10b.

The engineering design and analysis process relies on measurements and data collected from the physical world. In this hands-on, project-based course, students will be introduced to concepts, mathematics, hardware, software, methods, and mindsets for making measurements, collecting and interpreting data, and conducting engineering experiments using the scientific method, with a focus on biomedical engineering applications. Following an orientation to the tradeoffs among precision, accuracy, reliability, error, cost, and accessibility in measurement, students will explore topics including electronic circuits and sensors, computer-based data acquisition, data visualization and representation, and experimental design. In the first half of the semester, students will conduct scaffolded projects applying concepts learned in class to measuring properties of the human body such as temperature, force, electrical activity, and walking gait. Students will then collaborate on a team project to design and build more elaborate biomedical instrumentation to collect and analyze data such as pulse, blood oxygen levels, blood pressure, or pulmonary function. Throughout, we will engage with the ethics of measurement and experimentation, explore ideas of frugal engineering, and learn social science research methods relevant to engineering design and analysis such as surveys and interviews. Usually offered every year.

ENGR 13a Modeling and Simulation
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Prerequisites: MATH 10a and PHYS 10a or higher, or permission of the instructor. PHYS 11a or 15a is strongly recommended.

Building models of physical systems is a critical aspect of science and engineering. While models are expressed through the languages of math and physics, developing a good mental picture of the system at hand requires drawing on experience. Towards providing students with this experience, this course will build connections between the theoretical, the experimental, and the designed. They will be guided through a structured series of labs on a variety of system classes including nonlinear mechanical systems, infectious disease dynamics, mass transport, and coupled oscillators. In three of the labs, students will not only analyze and model a physical system but also use digital fabrication (3D printing, laser cutting, or CNC milling) to build and test physical versions of their models. This course is intended as a first exposure to modeling. Prior experience in programming is not required. Students will receive Python notebooks for each lab to be used for data analysis, numerically solving dynamical models, fitting models to data, and visualizing results. Practical coding skills, such as debugging, elaborating notebooks and learning to leverage open-source software, will be taught in a lab environment where students and the instructor can readily collaborate and solve challenges. Usually offered every year.

ENGR 22b Engineering a Circular Economy
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The way we produce, use, and dispose of materials and products today is unsustainable. Resource extraction destroys ecosystems and biodiversity worldwide; manufacturing is responsible for an enormous fraction of global greenhouse gas emissions; and waste plastics are now found in every corner of the earth, including our bodies, with as-yet unknown consequences to human and ecological health. The circular economy is a model of production and consumption that offers a potential solution to these problems -- where all materials and products are designed to be used, reused, and recycled again and again, minimizing environmental impact from resource extraction, manufacturing, use, and final disposal.

In this class, students will learn what is required to realize this vision of a circular economy from an engineering and design perspective. Based on a methodological foundation from industrial ecology, students will use life-cycle assessment and material flow analysis to characterize the profound issues with contemporary manufacturing and waste systems, and justify the principles of materials and product stewardship that underpin the circular economy model. Students will also learn to critique materials management and circular economy proposals at various scales, including materials and product design, so-called "circular business models," and municipal, national, and global materials systems. Finally, students will use what they have learned to propose new engineering design solutions to real-world challenges. Usually offered every second year.

PHYS 10a Introduction to Physical Laws and Phenomena I
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Usually taken with PHYS 18a.

An introduction to Newtonian mechanics, kinetic theory, and thermodynamics. Usually offered every year.

PHYS 10b Introduction to Physical Laws and Phenomena II
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Usually taken with PHYS 18b.

An introduction to electricity and magnetism, optics, special theory of relativity, and the structure of the atom. Usually offered every year.

PHYS 11a Introductory Physics I
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Corequisite: MATH 10a or the equivalent. Usually taken with PHYS 19a.

An introduction to Newtonian mechanics with applications to several topics. Usually offered every year.

PHYS 11b Introductory Physics II
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Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19b. Prerequisite: PHYS 11a or equivalent.

An introduction to electricity and magnetism and the special theory of relativity. Usually offered every year.

PHYS 12b Algorithmic Art
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Prerequisite: MATH 10a.

Snowflakes, flower petals, the spiral arms of a galaxy, waves and dunes, the stripes on a tiger--all are examples of naturally occurring patterns. While a beautiful pattern appeals to the aesthetic side of our brains, it also begs the question of whether we can recreate such artful designs. Hence, there is a motivation to understand beauty with logic.

Mathematics provides us with tools to characterize patterns, and physics teaches us how to understand the emergence of patterns. This course will help you learn some selected topics in math and physics that you will use to create designs. You will learn to use computer programming to materialize these abstract concepts into powerful visuals. We will start our algorithmic art journey by discussing basics of coding, coordinate geometry, matrix algebra, and using each of these concepts to create something beautiful. Then we will move on to more advanced topics like cluster finding algorithm, differential equations and random walks, and use these sophisticated tools to make art.

This interdisciplinary, interactive course will encourage creativity and teach you many transferrable skills like coding, collaboration, deconstruction of a complex problem into simple parts, communication of ideas by visual means, and teamwork, all of which are useful skills for various types of projects. Towards the end of the semester, you will hear talks from professional artists about their approach to art. As students exploring visual art within the field of science, these talks will enrich our own understanding of beauty and aesthetics and teach you new concepts to apply in your own unique way in the creation of original science-inspired art. Special one-time offering, spring 2024.

PHYS 15a Advanced Introductory Physics I
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Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19a.

An advanced version of PHYS 11a for students with advanced preparation in physics and mathematics. An introduction to Newtonian mechanics with special applications to several topics. Usually offered every year.

PHYS 15b Advanced Introductory Physics II
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Prerequisite: PHYS 11a or PHYS 15a or the equivalent, and MATH 10b or equivalent, or permission of instructor. Usually taken with PHYS 19b.

An advanced version of PHYS 11b for students with good preparation in physics and mathematics. An introduction to electricity and magnetism and the special theory of relativity for students with advanced preparation. Usually offered every year.

PHYS 18a Introductory Laboratory I
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Corequisite: PHYS 10a. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10a. Usually offered every year.

PHYS 18b Introductory Laboratory II
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Corequisite: PHYS 10b. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10b. Usually offered every year.

PHYS 19a Physics Laboratory I
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11a and 15a. Introductory statistics and data analysis including use of microcomputers and basic experiments in mechanics. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 19b Physics Laboratory II
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11b and 15b. Basic experiments in electricity, magnetism, and optics. Basic electrical measurements. Determination of several fundamental physical constants. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 20a Waves and Oscillations
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Prerequisites: PHYS 11a, PHYS 11b or PHYS 15a, PHYS 15b or permission of the instructor.

A survey of phenomena, ideas, and mathematics underlying modern physics-special relativity, waves and oscillations, and foundations of wave mechanics. Usually offered every year.

PHYS 29a Electronics Laboratory I
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Prerequisites: PHYS 11a, b or PHYS 15a, b; and PHYS 19a, b or permission of instructor. Students without a background in Physics should contact the instructor to discuss course requirements and receive permission to enroll.

Introductory laboratory in electronics. Topics to be covered are time constants, frequency response, rectification, amplification, radio reception, combinatorial logic, digital state machines, and analog-to-digital conversion. The class will solve first and second order differential equations directly and with the help of the complex exponential. Usually offered every spring.

PHYS 30a Electromagnetism
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Prerequisite: PHYS 20a and PHYS 31a, or permission of the instructor.

The fundamentals of electromagnetic theory. Includes electrostatics, magnetostatics, electric and magnetic circuits, and Maxwell's equations. Usually offered every year.

PHYS 31a Quantum Theory I
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Prerequisites: PHYS 20a and either PHYS 11a and b or PHYS 15a and b, or permission of the instructor.

Introduction to quantum mechanics: atomic models, Schrödinger equation, angular momentum, and hydrogen atom. Multielectron atoms and interaction of atoms with the electromagnetic field. Usually offered every year.

PHYS 31b Quantum Theory II
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Prerequisite: PHYS 31a.

A continuation of PHYS 31a. Topics include time-independent and time-dependent perturbation theory, identical particles, with applications to atomic, nuclear and condensed matter physics, scattering theory, and special topics as time allows. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 40a Introduction to Thermodynamics and Statistical Mechanics
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Prerequisite: PHYS 20a or permission of the instructor.

Studies the properties of physical systems as predicted by the statistical behavior of their constituent particles. Statistical mechanics provides a molecular-level interpretation of macroscopic thermodynamic quantities such as work, heat, free energy, and entropy. Topics studied will include; the laws of Thermodynamics, semi-classical and quantumstatistical mechanics, ensembles (microcanonical, canonical, and grand canonical), thermodynamic potentials and applications to a number of different systems. Usually offered every year.

PHYS 91g Introduction to Research Practice

Prerequisite: Student must complete online safety training relevant to the research group. Offered exclusively on a credit/no-credit basis. Yields quarter-course credit. May be repeated for credit.

Students engage in Physics research by working in the laboratory of a faculty member for a minimum of 3 hours per week for one semester. Students who have declared a Physics major must receive permission from the Physics Undergraduate Advising Head as well as the faculty sponsor to enroll in PHYS 91g. Usually offered every year.

PHYS 92a Research Internship, Off-Campus

Prerequisite: Permission of the undergraduate advising head.

Same as PHYS 93a but work is performed off-campus. Work done off-campus must be presented in the same forms to the appropriate research group during the semester following completion of the work. Usually offered every year.

PHYS 93a Research Internship

Prerequisite: Permission of the undergraduate advising head required.

The physics research internship provides students with an opportunity to work in a research setting for one semester, on-campus, pursuing a project that has the potential to produce new scientific results. Student and faculty members mutually design a project that supports the research agenda of the group. Students must attend all research group meetings and present their findings in oral and written form at the end of the semester. The project typically includes theoretical, computational, and/or laboratory research, and may involve collaboration with other group members. In some cases, credit toward the physics laboratory requirement may be given. Course requires signature of the instructor, is subject to the availability of undergraduate research positions, and is typically open only to juniors and seniors. Usually offered every year.

PHYS 97a Tutorial in Physics

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

PHYS 97b Tutorial in Physics

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

PHYS 98a Readings in Physics

Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

PHYS 98b Readings in Physics

Yields half-course credit. Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

NPHY 115a Dynamical Systems
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Prerequisites: MATH 10a, b or equivalent; MATH 15a and/or some coding experience would be helpful.

An introduction to the theory of nonlinear dynamical systems, including bifurcations, limit cycles, chaos, and coupled oscillators. Covers analytical, computational, and graphical methods of solving sets of nonlinear ordinary differential equations, as well as mathematical modeling of natural phenomena. Examples will be drawn from physics, chemistry, population biology, and neuroscience. Usually offered every third year.

PHYS 100a Classical Mechanics
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Prerequisites: PHYS 20a or permission of the instructor.

The goal of this course is to engage students in an exploration of classical mechanics from a modern perspective. Students are expected to have familiarity with Newtonian Mechanics, and have taken a calculus-based mechanics course. Usually offered every second year.

PHYS 102a General Relativity
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Prerequisites: PHYS 20a or permission of instructor.

An introduction to the basic principles of general relativity. Topics include a review of special relativity, tensor analysis in curved space-times, the principle of equivalence, the Einstein equations, the Schwarzschild solution, and experimental tests of general relativity. Usually offered every second year.

PHYS 104a Condensed Matter Physics
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Prerequisite: Phys 40a or permission of instructor.

Mechanical, thermal, and electronic properties of matter including fluids, solids, liquid crystals, and polymers. Simple models of matter are developed and used to discuss recent experimental findings. Usually offered every second year.

PHYS 105a Biological Physics
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Physical forces in living matter are studied from the perspective offered by statistical mechanics, elasticity theory, and fluid dynamics. Quantitative models for biological structure and function are developed and used to analyze systems such as single molecule experiments, transcriptional regulation networks, the forces arising during DNA packaging in a virus, and mechanisms underlying mammalian pattern formation. Usually offered every second year.

PHYS 107b Particle Physics
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Prerequisite: PHYS 30a or permission of the instructor. Corequisite: PHYS 31a (formerly PHYS 30b) or permission of the instructor.

The phenomenology of elementary particles and the strong, weak, and electromagnetic interactions are studied. Properties of particles, quarks, neutrinos, vector bosons, Higgs particles, supersymmetry, symmetries, and conservation laws are covered. This course is co-taught with the graduate course PHYS 167b, and the workload will be appropriate to each group. Usually offered every second year.

PHYS 108b Astrophysics
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Prerequisites: Physics 20a or permission of instructor.

Application of basic physical principles to the study of stars, galaxies, quasars, and the large-scale structure of the universe. Usually offered every second year.

PHYS 110a Mathematical Methods for the Sciences
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Prerequisite: PHYS 30a, PHYS 31a, or permission of the instructor.

Studies mathematical techniques that arise in the context of continuum mechanical (fluids and elastic media). Subjects include vector and tensor calculus, differential geometry, differential equations, and dimensional analysis. Usually offered every other year.

PHYS 111a Physical Continuum Mechanics
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Prerequisites: PHYS 30a, PHYS 31a, or permission of the instructor.

Studies physics of continuous media, focused on fluid mechanics or the theory of elasticity. Subjects include: basic equations; simple static solutions; small pertubations / wave equations; dislocations in elastic media; instabilities and turbulence in fluids; biophysical and geophysical applications. Usually offered every second year.

PHYS 159b Programming in Physics
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Aimed at students who are looking to learn how to write high quality object-oriented code for physics simulations. In this class, you will learn how to write code that is readable and easily passed to other scientists. How to write tests for your code to be confident in its behavior and how to structure your code so it is easy to add new measurements or simulation features. We will use specific physics applications to demonstrate these concepts; additional applications related to each student’s area of research or interest will be chosen for the final projects. Usually offered every year.

PHYS 161a Electromagnetic Theory I
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Electrostatics, magnetostatics, Maxwell’s equations, electromagnetic waves. Usually offered every year.

PHYS 161b Electromagnetic Theory II
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Radiation. Relativistic dynamics. A selection of other topics such as electromagnetism in matter, optics, and field quantization. Usually offered every second year.

PHYS 162a Quantum Mechanics I
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Lagrangian and Hamiltonian classical mechanics; fundamentals of nonrelativistic quantum theory and its application to simple systems; quantum entanglement and quantum statistical mechanics. Usually offered every year.

PHYS 162b Quantum Mechanics II
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Path integral formulation of quantum mechanics. Quantum treatment of identical particles. Approximate methods: variational, WKB, and perturbation theory. Applications to atoms, molecules, and solids. Usually offered every year.

PHYS 163a Statistical Physics and Thermodynamics
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Prerequisite: PHYS 40a, or graduate level standing.

The thermal properties of matter. Derivation of thermodynamics from statistical physics. Statistical theory of fluctuations. Phases and phase transitions. Usually offered every year.

PHYS 163b Principles of Soft Materials Theory
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Prerequisite: PHYS 163a or the equivalent.

Introduces non equilibrium statistical mechanics and applications of equilibrium and non equilibrium statistical mechanics to understanding emergent phenomena in soft materials such as colloids, polymers and liquid crystals. Usually offered every second year.

PHYS 164a First Year Tutorial I
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Yields half-course credit.

A review of physics from the most elementary topics to those treated in other first-year graduate courses. The environment of an oral qualifying examination is reproduced in the tutorial. Usually offered every year.

PHYS 167b Particle Phenomenology
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The phenomenology of elementary particles and the strong, weak, and electromagnetic interactions. Properties of particles, kinematics of scattering and decay, phase space, quark model, unitary symmetries, and conservation laws. This course is co-taught with PHYS 107b, and the workload will be appropriate to each group. Usually offered every second year.

PHYS 168b Introduction to Astrophysics
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Bremsstrahlung, synchrotron radiation, inverse Compton scattering. Extended and compact radio sources, jets, superluminal motion. Quasars and active galactic nuclei, IR to X-ray continua, spectral line formation. Black holes and accretion disks. Cosmology. Usually offered irregularly as demand requires; consult department.

PHYS 169b Advanced Laboratory
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Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three or four experiments during the term. This course is co-taught with PHYS 39a. Usually offered every year.

PHYS 202a Quantum Field Theory

Prerequisite: PHYS 161a and PHYS 162a, or permission of the instructor.

Methods of statistical and quantum field theory, including path integrals, second quantization, Feynman diagrams, renormalization group, epsilon expansions, effective field theory. Applications ranging from phase transitions and critical phenomena to gauge theories of particle physics. Usually offered every second year.

PHYS 204a Condensed Matter II

Modern techniques such as effective field theory, scaling, and the renormalization group are introduced and used to study solids, magnets, liquid crystals, and macromolecules. Most of the theory is developed on simple models and applied experiments. Usually offered every second year.

PHYS 212a Introduction to Research I

Open to first year graduate students in Physics.

Supervised introductory research, consisting of advanced readings in the primary literature and/or introductory lab work. The student will meet with the instructor weekly to discuss the reading or work, attend group meetings and seminars, and present a short written report and oral presentation at the end of the semester. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 212b Introduction to Research II

Open to first year graduate students in Physics.

Supervised introductory research, consisting of advanced readings in the primary literature and/or introductory lab work. The student will meet with the instructor weekly to discuss the reading or work; attend group meetings and seminars; and present a short written report and oral presentation at the end of the semester. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 213a Advanced Examination Tutorial I

Supervised preparation for the advanced examination. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 213b Advanced Examination Tutorial II

Supervised preparation for the advanced examination. Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 280a Advanced Readings

Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 280b Advanced Readings

Specific sections for individual faculty members as requested. Usually offered every year.

PHYS 300a Master's Thesis

Instructor and DGS permission required.

Students who have selected and received approval from the faculty member supervising the thesis and the Director of Graduate Study, may enroll in this thesis course with their faculty supervisor. The thesis consists of reading some advanced mathematics material in the form of topics books or a series of research articles, writing a thesis on a topic, and presenting the results of your reading and research during an oral presentation at the end of the semester. Usually offered every year.

PHYS 393g Graduate Research Internship

Permission of the graduate program director required. Yields quarter-course credit. May be repeated for credit. For Ph.D. students only.

Offers Ph.D students an opportunity to engage in industrial research in a field which enhances their dissertation research topic in physics by completing a paid or unpaid internship of at least ten weeks duration and forty hours per week, approved and monitored by a faculty member. Usually offered every summer.

PHYS 401a Dissertation Research

Independent research for the PhD. Specific sections for individual faculty members as requested. Usually offered every semester.

PHYS 401b Dissertation Research

Independent research for the PhD. Specific sections for individual faculty members as requested. Usually offered every semester.

PHYS 18a Introductory Laboratory I
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Corequisite: PHYS 10a. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10a. Usually offered every year.

PHYS 18b Introductory Laboratory II
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Corequisite: PHYS 10b. May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10b. Usually offered every year.

PHYS 19a Physics Laboratory I
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11a and 15a. Introductory statistics and data analysis including use of microcomputers and basic experiments in mechanics. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 19b Physics Laboratory II
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May yield half-course credit toward rate-of-work and graduation. Two semester-hour credits.

Laboratory course designed to accompany PHYS 11b and 15b. Basic experiments in electricity, magnetism, and optics. Basic electrical measurements. Determination of several fundamental physical constants. One afternoon or evening of laboratory per week. One one-and-a-half-hour lecture per week. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

PHYS 39a Advanced Physics Laboratory
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Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

PHYS 99d Senior Research

Permission of the undergraduate advising head required.

Original research under the direction of a faculty committee. A written thesis and oral defense are required. The complete set of rules is available from the physics department office. Usually offered every year.

BCBP 200b Reading in Macromolecular Structure-Function Analysis

Introduces students to chemical and physical approaches to biological problems through critical evaluation of the original literature. Students analyze scientific papers on a wide range of topics in the fields of biochemistry and biophysics. Discussion focuses on understanding of the scientific motivation for and experimental design of the studies. Particular emphasis is placed on making an independent determination of whether the author's conclusions are well justified by the experimental results. Students are also introduced to grant-proposal writing by preparing NIH-format mock proposals for critical discussion and evaluation. Usually offered every year.

ENGR 11a Introduction to Design Methodology
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Prerequisite: Instructor permission required.

An introduction to the engineering design process, with a focus on human-centered design. Students work in teams to solve authentic design problems under the theme of “design to repair the world.” Students are guided through a highly scaffolded process in which they form an idea, sketch it, and develop it through multiple iterations leveraging quick feedback loops and the Design Thinking methodology. Students will become fluent in basic additive and subtractive manufacturing, including 3D printing, laser cutting, and CNC machining. Usually offered every year.

ENVS 110a Data Analysis for Environmental Studies
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People in environmental fields increasingly need career-ready technical skills for managing, analyzing, and representing diverse types of data. The goal of this course is to engage students in authentic work with environmental data through a combination of collaborative, hands-on Python programming and project-based learning. Usually offered every year.

QBIO 110a Numerical Modeling of Biological Systems
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Prerequisite: MATH 10a and b or equivalent.

Modern scientific computation applied to problems in molecular and cell biology. Covers techniques such as numerical integration of differential equations, molecular dynamics and Monte Carlo simulations. Applications range from enzymes and molecular motors to cells. Usually offered every second year.

QBIO 120b Quantitative Biology Instrumentation Laboratory
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Focuses on optical and other instruments commonly used in biomedical laboratories to make quantitative measurements in vivo and in vitro. Students disassemble and reconfigure modular instruments in laboratory exercises that critically evaluate instrument reliability and usability and investigate the origins of noise and systematic error in measurements. Usually offered every year.