Natural Sciences & Mathematics

This biology core class is a theme-based, lecture and discussion course that covers unifying concepts in the biological sciences. Several sections of this course will be offered, with each section covering topics within a specific discipline of biology. Major themes will be consistent in each section offering, including historical aspects, principles of evolution, understanding science as "a way of knowing" and others, but most important is the connection made among people, the environment, society, and the scientific process used to discover what we know. Each section will incorporate supplemental resources in lieu of standard textbooks to make the course a unique liberal arts experience and to establish connections with other areas of the core curriculum. Some sections may also have laboratory components, demonstrations, or field trips to complement what is being taught in the lecture.
Does not count towards the biology major or minor.

An introduction to cellular structure and function, and the biochemical basis for life and genetic control of the cell. This course covers fundamental cellular processes such as replication, transcription, translation, inheritance, gene expression, photosynthesis, and respiration. Laboratory work is included. Required in the field of concentration.

An introduction to the major taxonomic groups of organisms and their phylogenetic relationships. This course applies cellular and genetic processes to the evolutionary mechanisms within organismal populations and the resultant biological diversity of life. Laboratory work is included. Required in the field of concentration

This course examines the characteristics of populations, communities and ecosystems in terms of energy flow, biogeochemistry and multivariate interactions (biotic and abiotic). The course will demonstrate the role of evolution in ecosystem composition, structure and function. The nature of the major North American Biomes will also be discussed with an emphasis on the importance of biodiversity and the interdependence of living things. Two weekend field trips are required. Also offered during the summer at the G.H. Gordon Biological Station. 

An introduction to the techniques and style of scientific writing. Required in the field of concentration. Must be taken before BIO 590. 

An introduction to vertebrate development, including studies of germ cells, segmentation, and growth of the principal tissues and organs. Laboratory work is included. 

The lecture will present an introduction to the major organ systems and their evolutionary history within vertebrates. The course will include a brief review of the diversity of vertebrates and their phylogenetic relationships. Emphasis will be placed on structural modifications and functional changes between vertebrate groups and how they are related to differences in environments and modes of life. The weekly two-hour laboratories will involve dissections of lamprey, sharks, cats, and observation of a pro-sected human cadaver. Offered occasionally.

The principles and mechanisms of function in animals and their constituent parts from molecules to organs. The course will consist of three lecture hours and two laboratory hours each week. Offered occasionally.

The study of plants as living organisms through a survey of the diversity in the plant kingdom. Emphasis will be placed on plant morphology, anatomy, classification, and evolution of structure and function in response to the environment. Laboratory work with fresh and preserved materials is included. 

The study of physiological processes in plants. Laboratory work is included. 

An advanced study in the plant sciences focused on understanding the concept and theories that govern the distribution and abundance of plant populations and communities. 

A study of the structure and function of the human body; fundamental processes including nervous function, hormones, integument, respiration, circulation, blood, muscles, and skeleton. Laboratory work is included. 

The study of the principles of heredity, gene function and mutation, and growth and reproduction.

An introduction to field biology with an emphasis on hands-on field research techniques. Very minimal lecture, and substantial time in forests, lakes, streams, and other habitats of northern Michigan. Field experiences will focus on experimental design, sampling terrestrial and aquatic organisms, population estimations, community interactions, ecosystem evaluations, and proper use of field research equipment. Offered at the G.H. Gordon Biological Station during the 2nd summer session.

The study of Michigan's native plants, including trees, shrubs, wildflowers, aquatic plants and grasses. Includes extensive field work and overnight field trips.

An introduction to the history of the earth from its formation to the present, including the development of the earthís interior, crust, oceans, climate, continents, mountains and glaciers. In addition to the abiotic history of our planet, prevailing scientific theories on the origins, evolution and diversity of life (from bacteria to dinosaurs) on earth will be examined. Emphasis is placed on developing skills in both spatial and temporal cognition. Lectures are enhanced by field trips. 

A study of the infrastructure and function of cells. Topics include the study of electron micrographs, cellular respiration, enzyme kinetics, mechanisms of movement, protein synthesis and the implications of cellular function in multicellular organisms. Laboratory work is included. 

An introduction to the study of the microscopic features of cells, tissues, and organs, the physiology that arises from that microanatomy, and laboratory techniques for the preparation of histological specimens. The course will emphasize the major organ systems and tissue types of mammals. 

An introduction to philosophy of science, logical structure of the scientific method, and principles of univariate statistics for the biological sciences. Laboratory work is included, which will require the mastering of a statistical software program. Must be taken before BIO 591. 

An overview of anthropogenic environmental degradation and solutions for achieving a sustainable planet. Topics include the history of conservation, economics and ethics, sustainable engineering and building, principles of ecology, overpopulation, world hunger, principles of soil science, agriculture, waste management, air and water pollution, climate change, habitat loss, and extinction. Course includes field trip opportunities for hands-on learning that can be applied to environmentally responsible homestead management. 

The study of microorganisms, focusing on bacteria and viruses. General topics include morphology, growth, reproduction, metabolism, mechanisms of genetic exchange, control, pathogenic and applied microbiology. Fundamental concepts of virology and immunology are also covered. Laboratory work includes isolation and identification techniques. 

An introduction to the ecology of inland waters, including lakes, ponds, wetlands, and streams. Major topics include geologic origins, typology, geographic distribution, biota, ecological succession, ecosystem function, and restoration/management. Emphasis is placed on the interaction between organisms and the environment. Laboratories include use of field equipment, field research techniques, and identification of aquatic organisms, including protozoa, invertebrates, fish, herpetofauna, and plants. Many laboratories will be conducted out of doors, and there is one required field trip off campus. 

An introduction to historical microbiology, microbial physiology, environmental microbiology, microbial genomics, and current trends in microbiology. The topics will be presented in an informal lecture/discussion format three days per week. Laboratories will emphasize individual and group projects covering aspects of bacterial photosynthesis, as well as selected laboratory exercises. 

Insects represent 80 percent of all animal species. This course examines their classification, anatomy, physiology, behavior, and ecology, as well as their positive and negative impacts on people and the effects of insect pest control. The laboratory will encompass both indoor activities and several field trips to local environments. 

The study of empirical, theoretical, and conceptual foundations of animal behavior. Laboratory experiments, emphasizing ethological methodology, as well as discussion, will reinforce these foundations. 

The lecture will present the diversity and biology of mammals from an evolutionary perspective. It will examine the diversity of living and extinct mammals and explore the mechanisms responsible for their evolution and extinction and will include discussion of mammal origins, evolution, phylogeny, paleontology, physiology, behavior, ecology and economic importance. There are approximately 4,600 living species of mammals that are spread throughout all the earth ís environments and make up 26 diverse orders, such as carnivores, whales, bats, rodents, and primates.  

A survey of animal parasites, including their taxonomy, structure, life histories, and evolution. Emphasis is on the practical implications of medical and veterinary parasitic diseases. 

The lecture will present both an introduction to theoretical studies, and discussion of actual molecular and phenotypic variation in natural populations and how processes such as mutation, recombination, and selection affect genetic variation. Topics discussed will include genetic variation, Hardy-Weinberg Equilibrium, genetic recombination, linkage and disequilibrium, basic natural selection models, molecular evolution and phylogenetics, mutation, genetic drift, inbreeding and nonrandom mating, population subdivision and gene flow, and the neutralist versus selectionist debate. 

This is primarily a course in human gross anatomy as it involves fours hours of directed cadaveric dissections each week. In addition to laboratory dissections, there will be weekly lectures on advanced topics in physiology. 

An introduction to the basic concepts of molecular biology: the nature, control, recombination and rearrangement of genes; gene manipulation; recombinant DNA (rDNA) techniques; and bioengineering strategies. Laboratory work is included. 

An advanced study of the human immune system. Lecture topics include the structure and function of the organs and cells of the immune system, immune system development, intrinsic and innate immunity, antigen recognition and presentation, adaptive immunity, immunological memory, immune system failure, autoimmunity, and allergies. 

Science as a way of knowing will be emphasized to understand how biology seamlessly fits within the liberal arts. This course will familiarize future secondary school teachers with the design, implementation, and evaluation of lectures, demonstrations, and laboratories. The goal is for any major to learn more about the field of biology, how best to build a foundation in biological understanding, and foster a sense of wonder about the natural world in their future students. This course may fulfill one of the elective requirements for the Classical Education minor.

An advanced study of the virosphere. Lecture topics include virus structure, replication cycles, categories of infection, pathogenesis, immune response and evasion, transmission, and treatment. A broad range of virus families are represented. 

An advanced study into the neurophysiology of human cognition. Topics, starting with basic neuroanatomy and neurophysiology, will build toward an understanding of cognitive functions, emphasizing sensory processing, memory formation, decision making, emotions, and brain diseases. Ultimately the course aims to help students link brain functions to modern views of consciousness. 

Introduction to research; group format. Required in the field of concentration. To be taken by majors in the fall semester of their junior year.

Exempt from tuition overload charges. 

Senior research project; group format seminar. Required in the field of concentration. To be taken by majors in the fall semester of their senior year.

Exempt from tuition overload charges. 

Individualized literature review leading to research proposal. Required in the field of concentration. To be taken by majors in the spring semester of their junior year.

Exempt from tuition overload charges. 

Capstone preparation, presentation, and defense of the senior research project. Required in the field of concentration. To be taken by majors during the spring semester of their senior year.

Exempt from tuition overload charges. 

Capstone preparation, presentation, and defense of the senior research project, plus a written thesis approved by the research advisor and an additional outside reader. Required of students pursuing department honors or those who have received LAUREATES funding. Optional for all other students. To be taken by majors during the spring semester of their senior year.

Exempt from overload tuition charges. 

The comprehensive biology examination is offered twice per year, typically at the beginning of fall and spring semesters. All biology majors must pass the exam in order to graduate. It is highly recommended that students take it during their final semester at Hillsdale.

Two four-hour courses in introductory chemistry. These courses cover fundamental laws and theories: the atom and its construction, the nature of the chemical bond, stoichiometry, phases of matter, solution chemistry, thermodynamics, kinetics, equilibria, electrochemistry, and an introduction to organic chemistry. Three lectures plus one two-hour laboratory per week in the fall, and three lectures plus one three-hour laboratory per week in the spring. Prerequisites: two years of high school mathematics plus high school chemistry are recommended. 

Two four-hour courses in introductory chemistry. These courses cover fundamental laws and theories: the atom and its construction, the nature of the chemical bond, stoichiometry, phases of matter, solution chemistry, thermodynamics, kinetics, equilibria, electrochemistry, and an introduction to organic chemistry. Three lectures plus one two-hour laboratory per week in the fall, and three lectures plus one three-hour laboratory per week in the spring. Prerequisites: two years of high school mathematics plus high school chemistry are recommended. 

Two four-hour courses in the general field of organic chemistry including reaction and preparations of both aliphatic and aromatic compounds, functional group approach to reactions, and the theoretical relationship of electronic structure to mechanisms. The laboratory will emphasize preparative methods. Designed for preprofessional students in allied health fields, as well as for students working in this field of concentration. Three lectures plus one laboratory period per week. CHM 303 is a prerequisite for CHM 304.

Two four-hour courses in the general field of organic chemistry including reaction and preparations of both aliphatic and aromatic compounds, functional group approach to reactions, and the theoretical relationship of electronic structure to mechanisms. The laboratory will emphasize preparative methods. Designed for preprofessional students in allied health fields, as well as for students working in this field of concentration. Three lectures plus one laboratory period per week.

A course devoted to the study of stereochemistry, mechanisms, multi-step syntheses and newer synthetic methods. Characterization of compounds will utilize spectroscopic methods. Emphasis is placed on recent and current developments in organic chemistry. Periodical literature is employed in addition to textbooks. Three lectures per week; some laboratory work may be required.

The theory, principles and practices of analytical chemistry involving statistical analysis, equilibria, acid-base chemistry, complexation, oxidation-reduction, spectroscopy, and electrochemistry. Quantitative determinations using gravimetric analysis, titrations (acid-base and complexiometric), and spectrophotometry are a part of the laboratory portion of this course. Three lectures plus one four-hour laboratory per week. 

An in-depth examination of techniques used to separate and analyze mixtures. Topics examined include gas and liquid chromatography, solid-phase extraction, dialysis and electrophoresis. Particular emphasis will be placed on liquid chromatography (ion chromatography, size exclusion, reversed-phase, normal-phase, affinity and chiral separations) and capillary electrophoresis (free solutions, gels, micellar and isoelectric focusing). Lecture with lab. 

Introduces an integrated analysis of the chemical structure, dynamic mechanisms, and cellular functions of proteins, nucleic acids, lipids, and carbohydrates. Topics will include enzymology, molecular biology, metabolism, and methodological theory. 

Detailed study of advanced topics in cellular signaling and metabolism. This course will focus on hormonal control mechanisms, signal transduction pathways, and enzyme mechanisms related to the citric acid cycle, oxidative phosphorylation, and the degradation and biosynthesis of sugars, fatty acids, amino acids and nucleotides. There will be an emphasis on understanding the primary literature and recent advances in the field of biochemistry. Three lectures per week. 

In this laboratory course, students will engage with methods and instrumentation common to research in biochemistry. Students will learn to modify protein sequences, express and purify proteins, and assess the function of proteins through kinetic and thermodynamic assays. Students will also design and implement an independent research project culminating in a primary literature-style paper based on their findings.

Students will meet in small groups with their faculty research mentors. Students will give presentations on background information, lab techniques, and previous research relevant to their research interests. They will formulate and write a research proposal with the aid of their faculty mentor and peer group, and will serve as critical reviewers of their peers' presentations and/or proposals. They will also attend several senior thesis presentations (CHM 575) and presentations by invited speakers from industry and academia. To be taken in the spring of the junior year by all biochemistry and chemistry majors. 

Exempt from tuition overload charges. 

A study of thermodynamics, kinetics, molecular structure and spectroscopy, with an emphasis on biological applications. The concepts of energy, enthalpy, entropy, chemical equilibrium, kinetics of complex reactions, dynamics of microscopic systems, chemical bonding, non-covalent interactions, optical spectroscopy and magnetic resonance will be covered in some detail, and the discussion will center on the importance of these concepts in the life sciences. Three lectures per week. 

An advanced treatment of chemical principles. Topics include quantum mechanics, atomic and molecular structure, origin of spectra, molecular orbital theory, computational chemistry, laser spectroscopy, and magnetic resonance. Three lectures plus one four-hour laboratory period per week. 

A continuation of CHM 502. Topics include statistical thermodynamics, first, second, and third laws of thermodynamics, thermochemistry, phase equilibria, chemical equilibria, molecular motion, chemical kinetics, photochemistry, and reaction dynamics. Three lectures plus one four-hour laboratory period per week. 

This course will expand on topics introduced in CHM 502 and 503. Course content will vary with each offering and will depend on the interests of enrolled students. Possible topics to be covered include computational chemistry, surface chemistry, advanced group theory and crystallography, advanced spectroscopy and nuclear chemistry. Three lectures per week; some laboratory work may be required. 

A course that includes lecture and laboratory work in basic electronics, flame atomic emission and absorption spectroscopy, UV-Vis and IR molecular absorption, luminescence methods, NMR spectroscopy, mass spectrometry, electrochemical analysis, and liquid and gas chromatography. Three lectures and one four-hour laboratory per week. 

Students will be provided information and guidance about writing and editing a successful senior thesis and giving an effective oral presentation on their research. More broadly, through readings, presentations, and discussions, students will be expected to reflect on their scientific knowledge and experience in the context of ethical, social, and philosophical considerations and implications. A variety of topics may be covered, including attributes of good science, ethics in science, faith and science, responsibilities of scientists in society, and the limitations of science. Students will submit an essay on a theme from the course (e.g., the place of science within the traditional liberal arts). They will also attend presentations by invited speakers from industry and academia. Students seeking Departmental Honors or an ACS-certified degree will compose an initial draft of their senior thesis. To be taken in the fall of the senior year by all biochemistry and chemistry majors.

Exempt from tuition overload charges. 

Each student will critically review the thesis of another member of the class (peer review). They will make necessary revisions to their own senior theses after peer review and review by their faculty research mentors. They will also give a formal oral presentation of their research to the department, and attend presentations by invited speakers from industry and academia. Each student will also serve as a mentor to a junior who is preparing a presentation for CHM 475. To be taken in the spring of the senior year by biochemistry and chemistry majors who are seeking Departmental Honors or an ACS-certified degree.

Exempt from tuition overload charges. 

Laboratory and/or literature research in advanced chemistry, designed to develop independent research skills through the guidance of a research mentor on a specific chemical problem. 

Introduction to linked lists, stacks, queues, maps, trees, binary search trees, graphs, and hashing. Emphasis is on writing readable, efficient, and maintainable code. Object-oriented programming techniques, dynamic memory management, exception handling, and abstract data types are studied. 

The nature of the logical foundation of the discipline is emphasized with coverage including propositional and predicate calculus, formal systems and proof, and methods of informal proof. Writing proofs about sets, functions, grammars, trees, and graphs is emphasized with an eye both towards the study of the logic itself as well as a deepening understanding of the structures at hand.

Introduction to the design and analysis of algorithms. Course coverage includes divide and conquer algorithms, dynamic programming, greedy algorithms, back-tracking, branch-and-bound, and classic searching and sorting. Complexity is studied as well and includes order of growth, tractability, P vs. NP, and how to design algorithms for NP-hard problems. 

Formal languages and automata theory, with an introduction to computability. Course coverage includes deterministic and nondeterministic automata, pushdown automata, regular and context-free languages and grammars, models of computation including the Turing machine, computability, decidability, and the Halting problem. 

Introduction to the architecture and organization of physical computers. Machine language programming, the design of instruction sets, and software/hardware tradeoffs are emphasized. Digital design topics such as transistors, Boolean algebra, logic gates, functional units, timing, computer arithmetic, and overall system design are studied. Topics include data path and controller design, hazard detection and resolution, dynamic scheduling, the memory hierarchy, parallelization, and application-specific processors. 

Microcontroller-based embedded system design and programming. Topics include basic machine electronics, interface design, and C and assembly language programming for real-time embedded systems. Applications to robotics such as planning, vision, and cybernetics are covered.

Introduction to applications-level software design principles with emphasis on writing efficient, maintainable, and reusable code. Topics include design patterns, debugging, testing, exception handling, recursion, memory management, classes, inheritance, and polymorphism. This is a programming intensive course giving the student experience in a modern object-oriented language.

Overview of basic ideas in artificial intelligence. Coverage includes knowledge representation, classic search techniques, probabilistic reasoning, and neural networks. Modern computer architectures supporting artificial intelligence algorithms are covered. Includes discussion of the nature of intelligence and whether machines can think. Prerequisite: CMP 101 and MTH 113/120

A course in modern machine learning via deep learning. Topics include statistical estimation, efficient gradient descent of nonlinear functions, convolutional models, attention-based models, and generative models. Emphasis is placed on maintaining a balance between theory and the ability to produce practically efficient implementation of these techniques leveraging GPU acceleration within a leading deep learning development framework. Practical implementation details also consider techniques for avoiding local optima and improving generalization.

Theory and application of stochastic, population-based, general-purpose problem solving algorithms inspired by natural evolution. Includes coverage of genetic algorithms, swarm intelligence, evolutionary algorithms, genetic programming, and multi-agent simulations. Applications to problems in science, engineering, mathematics, business, and the humanities are studied. Prerequisite: CMP 101 and MTH 113/120

The first of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the concepts of functions, limits, continuity and differentiation, exploring them in the context of algebraic functions. Prerequisites: none. 

The second of a two-semester sequence designed to introduce the ideas and applications of the Differential Calculus. This course focuses on the Differential Calculus of transcendental functions, including exponential, logarithmic and trigonometric functions. The course will introduce integration including the Fundamental Theorem of Calculus. The successful completion of MTH 113 is equivalent to successful completion of Calculus I. 

A comprehensive study of limits, continuity and differentiation of functions of one real variable and their applications. Introduction to integrals. Credit will not be granted for both MTH 113 and MTH 120. Prerequisites: For students in their first two years of college and an ACT mathematics score of 27 or higher. 

A continuation of MTH 120. Techniques and applications of integration. Infinite sequences and series. 

A thorough treatment of the techniques of formal reasoning. Topics include truth-functional logic, quantification logic and construction of correct deductions.

The theory and applications of vector spaces, matrix algebra, linear transformations and eigenvalues. 

A third-semester calculus course. Topics will include vectors and three-dimensional coordinate systems, partial differentiation with applications, multiple integrals, and vector calculus. 

Properties of the integers, the Euclidean Algorithm, divisibility, Diophantine equations, prime numbers, congruences and residues. 

An introduction to the theory and applications of discrete mathematics. Topics for the course include proof writing, logic, set theory, induction, recursion, combinatorics, relations, functions, and graph theory.

A study of the techniques and theory of solving ordinary and partial differential equations. Topics may include series solutions, numerical methods, Fourier and Laplace transforms, linearization, stability theory, periodic orbits, and bifurcations and chaos. Prerequisite: MTH 310 or PHY 304. Spring, typically odd-numbered years.

A college-level approach to Euclidean and non-Euclidean geometries. The course will pursue an in-depth investigation into the following topics: Hilbert's postulates for Euclidean geometry, the parallel postulates, neutral geometry and non-Euclidean geometry. 

Introduction to the mathematical theory of probability. Discrete probability spaces, conditional probability, discrete and continuous random variables, expectations and distributions.

Game theory is the study of the interaction of rational decision makers. This course uses game theory to study incentives and strategic behavior in practical situations of inter-dependent decision making and negotiations. The course will develop basic theoretical concepts in tandem with applications from a variety of areas, including bargaining, competition, and strategic voting. 

This course serves as an introduction to the formulation, analysis and interpretation of mathematical models in the study of problems in the natural, management and social sciences. Topics may include optimization, dimensional analysis, Markov chains and autonomous systems. The course will require the use of the Eaton Corporation Computer Laboratory and the software packages R, Mathematica, and Matlab. 

A course on mathematical interest theory. Topics discussed will include the time value of money, annuities and cash flows, loans, bonds, the yield rate of an investment, the term structure of interest rates, duration, and immunization. The course may also include topics from financial economics. Offered as needed.

A study of the historical development of various branches of mathematics from antiquity through the end of the nineteenth century. Topics include mathematics prior to classical antiquity, mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of the calculus, and the nineteenth century evolution of algebra, geometry, and analysis. The course will emphasize primary source materials. 

An introduction to proof writing, oral presentations, literature research, and computer software applied to mathematics. Offered as needed.

A rigorous treatment of the calculus of one variable, including limits, continuity, sequences, differentiation and Riemann integrals. This course should be taken in the junior or senior year. 

The theory of functions of a single complex variable. Complex numbers, elementary complex functions, differentiation and integration of complex functions, complex series and residue theory.

Numerical methods for approximation of roots, systems of linear equations, interpolation and curve fitting, numerical integration and differentiation, and differential equations. Problems are generally approached through structured algorithms. 

An introduction to the theory of algebraic structures, including the elementary properties of groups, rings and fields. This course should be taken in the junior or senior year. 

This course serves as a sequel to MTH 370 (Theory of Probability), focusing on the application of concepts introduced in MTH 370 to the theory and practice of statistical inference. Emphasis will be placed both on the mathematical theory underlying the definition and evaluation of various estimators and statistical tests, as well as the application of this theory to the analysis of real-world data sets. 

An introductory course in the fundamental concepts of general topology, including metric spaces, topological spaces, connectedness and compactness. 

Students will be introduced to contemporary mathematics literature with an emphasis on undergraduate research. Instruction will be given on how to read and write mathematics papers, how to give and receive math talks, what to do at math conferences, how to perform literature searches, and other skills related to the mathematics profession and the practice of mathematics beyond the classroom. 

An introduction to mechanics and waves. The class has three hours of lecture, two hours of laboratory investigation, and one hour of recitation per week. Recommended for the general student, those who have not taken high school physics, and science students who do not take calculus. Prerequisites: competence in algebra, geometry and trigonometry. (Physics and Chemistry majors, see PHY 201-202.)

An introduction to thermodynamics, electricity, magnetism, light, and optics. The class has three hours of lecture, two hours of laboratory investigation, and one hour of recitation per week. Recommended for the general student, those who have not taken high school physics, and science students who do not take calculus. Physics and Chemistry majors, see PHY 201-202.

An introduction to mechanics and waves. There are two hours of laboratory investigation, three hours of lecture, and one recitation per week. Recommended for science and mathematics majors. Required in the field of concentration.

An introduction to thermodynamics, electricity, magnetism, light and optics are taught in 202. There are two hours of laboratory investigation, three hours of lecture, and one recitation per week. Recommended for science and mathematics majors. 

An introduction to oscillations, waves, light, and Einstein's relativity, one of the two major advances in physics in the 20th century. Topics include: simple harmonic motion, damped oscillations, forced oscillations and resonance, coupled oscillations and normal modes, standing waves and traveling waves, Fourier analysis, sound, dispersion, electromagnetic waves, polarization, Poynting vector, radiation pressure, the generation of electromagnetic waves, scattering, reflection and refraction, geometrical optics, waveguides, interference, and diffraction. Topics in relativity include the postulates of special relativity; consequences for simultaneity, time dilation, and length contraction; Lorentz transformations; relativistic paradoxes; Minkowsky diagrams; invariants and four vectors; relativistic momentum and energy; particle collisions; relativity and electromagnetisms. Required in the field of concentration. 

An introduction to modern physics, including the second major advance in physics in the 20th century: Quantum Mechanics. Quantum Mechanics is discussed using the Schrodinger Equation. Solutions will give the wave function and energy level quantization of example systems: particles in potential wells, tunneling through barriers, harmonic oscillators, and the hydrogen atom. Discussion will progress to the properties of multi-electron atoms, the periodic table, X-ray spectra, and entanglement. Solids and molecules are discussed including bonding, molecular spectra, crystal structure, energy bands, the nature of metals, semiconductors and insulators, and how semiconductor devices work. We will then proceed to the basics of nuclear physics such as nuclear binding, models of the nucleus, nuclear spin, NMR and MRI, nuclear stability and radiation, radioactive dating, biological effects of radiation, and nuclear fission and fusion. Particle physics discussions will lead to elementary particle properties, particle accelerators, the standard model, and the history of the universe. Mathematical tools needed in upper-level classes are introduced as time allows. 

Modern physics lab emphasizing experimental techniques. Experiments focus on modern physics and will include blackbody radiation, the photoelectric effect, atomic spectra, Michelson interferometer, properties of laser light, single-photon detection, double-slit experiment done with single photons, Franck-Hertz experiment, etc. Experimental skills will be emphasized including error analysis, error propagation, least squares curve fitting, and hypothesis testing using the chi-square statistic. Required in the field of concentration.

This course will continue work on statistical concepts in data and error analysis, scientific report writing, and measurement procedures. Experiments are chosen from various areas of classical, quantum mechanical, atomic, and solid-state physics, e.g., oscillations, superconductivity, hydrogen atom wavefunctions, quantum control of proton resonance, energy band structure of solids, photoelectric effect, X-ray diffraction, and spectrometry. Required in the field of concentration.

Computer techniques and methods to solve physical problems are taught. Students will be introduced to Linux-based computing using the Python programming language. These tools will be employed in the study of problems such as integration techniques, Lissajous figures, Lagrange points, spacecraft trajectories, and N-body simulations. The Python skills acquired will be applicable to scientific computing in any natural science. Examples chosen will reflect the student's background and interests. Offered on demand.

Lectures deal with the understanding, design and use of basic electronic circuits, including passive networks, transducers, current and voltage amplifiers. The fundamentals of transistors, operational amplifiers, digital logic and scientific instrumentation circuits are described. Experimental work covers transistors, current and voltage sources, operational amplifier applications, timers, transducers, digital logic and computer circuits. Emphasis is on using integrated circuits. The course includes two hours of lecture and four hours of laboratory work per week. Required in the field of concentration. 

Three-hour course basic to advanced work in physics, chemistry and mathematics. Dealing with both statics and dynamics, Newtonian, Lagrangian, and Hamiltonian formalisms are examined, and concepts necessary to relativity and quantum mechanics are included. Some topics covered are motion with viscous forces and applications of mathematics (i.e., vector analysis and differential equations) 90 to the solution of physical problems.

Three-hour course basic to advanced work in physics, chemistry and mathematics. Dealing with both statics and dynamics, Newtonian, Lagrangian, and Hamiltonian formalisms are examined, and concepts necessary to relativity and quantum mechanics are included. Some topics covered are motion with viscous forces and applications of mathematics (i.e., vector analysis and differential equations) 90 to the solution of physical problems. Offered on demand.

A study of thermal and statistical physics incorporating a survey of classical thermodynamics. Topics include a statistical treatment of entropy, temperature, thermal radiation, chemical potential, and Helmholtz and Gibbs free energy. The Boltzmann, Planck and Gibbs distributions as well as ideal, Bose and Fermi gases are considered. Applications are made to metals, semiconductors, superconductors and astrophysics. 

The course will discuss the basic components of a physics high school course: lecture, demonstrations, laboratories. It will do this amid higher level discussions of what physics actually IS, how physics fits, or can and should fit, into a classical curriculum or curriculum taught at many Barney Charter Schools, and how effectively to make connections to the broader curriculum. Through this course, students will also acquire a set of tools such as lecture outlines, demonstrations, lab equipment lists, reading lists, etc. that they can take and use as a foundation for their future physics course. This course would be for any student who is considering going into science teaching in secondary education. This course fulfils one of the elective requirements for the Classical Education minor. Offered on demand

An essential study of electric and magnetic phenomena, with emphasis on the fields in vacuo and in materials. Vector calculus is introduced and then applied throughout. Electrostatics and magnetostatics are developed, with emphasis on Gauss' and Ampere's laws. Induced EMFs and Maxwell's equations conclude this basic course. Required in the field of concentration. 

Advanced laboratory experiments on topics from mechanics and light. Typical experiments include the speed of light, electron spin resonance, charge on the electron (Millikan experiment), driven harmonic motion, measurement of g(reversible pendulum), measurement of G (Cavendish torsional pendulum), Frank-Hertz experiment, optical interference effects in single and multiple slits, Michelson interferometer, Fabry-Perot interferometer, optical filter transmission characteristics, electron diffraction on graphite crystals, photoelectric effect, Schlierens optical system, and optical properties of prisms. (One course chosen from PHY 470, 471, 472 or 480 is required for the major.) 

A state-of-the-art X-ray diffractometer will be used to teach crystallography. The course stresses principles and measurement of atomic crystalline arrangements. Identification and physical properties of metals, inorganics, minerals, etc., will be considered. The second part of the laboratory will use gamma ray spectrometry to measure and identify nuclear isotopes. Principles of nuclear radiation and its detection will be taught. Both the X-ray and nuclear equipment use computer data collection and analysis. Radiation measurement may be studied to a greater extent as an option for those with corresponding career interests. (One course chosen from Physics 470, 471, 472, or 480 is required for the major.) 

Advanced laboratory experiments: electrostatic measurements, magnetic hysteresis, Hall effect, inductance, A.C. circuits, etc. (One course chosen from PHY 470, 471, 472 or 480 is required for the major.) Offered on demand.

This course involves an introduction to the magnetism of metals and alloys and magnetic impurities in these systems. In the first semester, 480, theoretical and experimental ideas in the areas of magnetism, condensed matter physics, low-temperature physics, and vacuum science will be discussed and demonstrated. The class will then carry out an experimental procedure for one alloy.  Research based on the theory and procedures learned in this class may be used for student research by taking PHY 481-3 below or with other arrangements.  This research is supported by an 8-Tesla superconducting magnet, a microbalance (0.1 micrograms), a low-temperature cryostat (3.8-300K), a helium leak detector, and high-vacuum equipment. A machine shop and other departmental equipment support the research. (One course chosen from PHY 470, 471, 472, or 480 is required for the major.)

In PHY 481- 483, the student will begin a series of measurements to contribute to the ongoing faculty-student research project. Four semesters of this work are possible. In addition, the student’s senior thesis may be based on the theory and procedures learned in PHY 480 and the student's further research in this area.
Offered on Demand.

The probabilistic theory of particles and their interactions has been very successful since its early forms treated quantization of radiation, electron-photon interactions, and atomic energies (Planck 1901, Einstein 1905, and Bohr 1913). Modern quantum mechanics deal with particles described as wave packets having a range of positions and momenta. This explains both the particle and wave effects observed. These wave packets are solutions of the Schrodinger wave equation and involve both space and time. The formal theory involves finding wave function solutions for harmonic oscillators, the hydrogen atom, and other systems. Physical properties of these systems are extracted from these wave functions using mathematical operators. This course is essential for those planning graduate study in physics or related areas. Required in the field of concentration.

Applications of Maxwell's equations to numerous practical situations in electrodynamics, including electromagnetic waves and radiation. The theory of relativity and its relation to classical electricity and magnetism are usually included. Strongly recommended for students who will go on to graduate studies in physics or engineering or who will study undergraduate electrical or electronic engineering. Offered on demand

An advanced study of nuclear and atomic physics. Topics will include: relativistic treatment of energy and momentum in nuclear reactions and Compton scattering, nuclear and atomic structure, the nucleonnucleon interaction, nuclear decay, particle accelerators, and nuclear particle detection. Quantum mechanics will be used when appropriate. Prerequisites: (One course chosen from PHY 507, 509, 511 or PHY 520 is required for the major.)

Background and theory necessary to understand modern optical devices, instruments, techniques and phenomena. The course begins with a study of the mathematics of waves and important aspects of Maxwell's electromagnetic theory. The course uses geometrical optics to understand thin and thick lenses and systems of lenses such as telescopes and microscopes. The wave theory of light is used to study polarization, interference and diffraction. Various types of interferometers are examined, as well as diffraction of multiple slits and gratings. (One course chosen from PHY 507, 509, 511, or PHY 520 is required for the major.) 

This course continues the study of Quantum Mechanics, building upon the foundations presented in PHY 490, Quantum Mechanics. Topics covered typically include identical particles, degenerate and nondegenerate time independent perturbation theory, the variational principle, the WKB approximation, time dependent perturbation theory, the emission and absorption of radiation, spontaneous emission, and scattering and partial wave analysis. These theories are applied to the fine structure of hydrogen, the Zeeman effect, hyperfine splitting, the ground state of helium, the hydrogen molecule ion and other systems. (One course chosen from PHY 507, 509, 511, or PHY 520 is required for the major.) 

A study of the properties and physical processes taking place in the solid. This subject draws on all the areas of physics and thus tends to unify knowledge from other courses. The course begins by laying the groundwork in crystal structure, crystal binding energies, crystal diffraction, and the reciprocal lattice. We will then consider the thermal properties of crystals, the free electron gas in metals, Fermi surfaces, energy bands in solids, electron transport, and semiconductor devices. Strongly recommended for those considering graduate school in physics, chemistry, or engineering, or seeking an industrial position in physics or engineering. (The physics major requires one course chosen from PHY 507, 509, 511, or PHY 520.)