Natural Sciences & Mathematics

An introduction to vertebrate development, including studies of germ cells, segmentation, and growth of the principal tissues and organs. Laboratory work is included. Prerequisites: BIO 200 and 201.

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. Prerequisites: BIO 200 and 201. 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. Prerequisites: BIO 200 and BIO 201.

The study of physiological processes in plants. Laboratory work is included. Prerequisites: BIO 200 and 201; BIO 305 is beneficial but not required.

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. Prerequisites: BIO 201 and 305, or consent of instructor. Offered alternating spring semesters.

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. Offered every spring semester. Prerequisites: BIO 200, CHM 201, and CHM 202.

The study of the principles of heredity, gene function and mutation, and growth and reproduction. Prerequisite: BIO 200.

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. Prerequisites: BIO 101 or equivalent. Offered every spring semester.

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. Prerequisites: BIO 200 and 201, CHM 201, and PHY 101. Offered alternating spring semesters.

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. Prerequisites: BIO 303 or BIO 308 or permission of instructor. Offered alternating spring semesters.

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. Prerequisites: MTH 105 and BIO 101 or equivalent. Required in the field of concentration. Must be taken before BIO 591. Offered fall and spring semesters.

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. Prerequisite: BIO 200. Offered every fall semester.

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. Prerequisites: BIO 200 and 360. Offered alternating spring semesters.

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. Prerequisites: BIO 201 or consent of instructor. Offered alternating fall semesters.

The study of empirical, theoretical, and conceptual foundations of animal behavior. Laboratory experiments, emphasizing ethological methodology, as well as discussion, will reinforce these foundations. Prerequisites: BIO 200 and 201. BIO 250 is strongly recommended. Offered alternating fall semesters.

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. Prerequisites: BIO 201 or consent of instructor.

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. Prerequisites: BIO 200 or 201 or consent of instructor. Offered every fall semester.

This is primarily a course in human gross anatomy with three hours of directed cadaveric dissections each week. Weekly lectures will include one laboratory recitation and two lectures on the structure and physiology of the digestive, renal, and reproductive systems. Prerequisite: BIO 308. Offered every fall semester.

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. Prerequisites: BIO 200 and 360, CHM 303, and PHY 101. Offered alternating spring semesters.

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. Prerequisite: BIO 360. Offered alternating fall semesters.

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. Prerequisite: BIO 360. Offered alternating fall semesters.

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. Prerequisites: BIO 200 and BIO 308 or PSY 333. Offered alternating fall semesters.

Senior research project; group format seminar. Required in the field of concentration. Prerequisite: BIO 340. To be taken by majors in the fall semester of their senior year.

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. Prerequisites: CHM 304 and BIO 202.

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. Prerequisites: CHM 452 and MTH 120.

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. Prerequisites: PHY 102 or 202, CHM 304 and MTH 220

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. Prerequisite: CHM 415 and 501 or 502

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

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

A continuation of MTH 120. Techniques and applications of integration. Infinite sequences and series. Prerequisite: MTH 113 or 120 with a grade of C- or better. Fall and spring, every year.

A thorough treatment of the techniques of formal reasoning. Topics include truth-functional logic, quantification logic and construction of correct deductions. Prerequisite: MTH 105 or higher mathematics course. Spring, even-numbered years.

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. Prerequisite: MTH 220. Fall, odd-numbered years.

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. Prerequisite: MTH 310 or MTH. Spring, typically even-numbered years.

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. Prerequisite: MTH 310. Spring, every year.

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. Prerequisite: MTH 220 with a grade of C- or better. 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. Prerequisites: MTH 310 and 320. Fall, even-numbered years.

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. Prerequisite: MTH 320. Fall, even-numbered years.

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. Prerequisite: MTH 310 and 320. Fall, every year.

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. Prerequisite: MTH 310 and and one of the following: MTH 330, MTH 335, or MTH 360. Fall, every year.

An introductory course in the fundamental concepts of general topology, including metric spaces, topological spaces, connectedness and compactness. Prerequisite: MTH 310 and one of the following: MTH 335 or MTH 360. Spring, even-numbered years.

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. Prerequisite: MTH 310 and MTH 320.

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. Prerequisite: PHY 202. Corequisites: PHY 310, MTH 320. Fall semester.

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. Prerequisite: PHY 303, 310 and MTH 320. Corequisite: PHY 311. Spring semester.

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, atomic, and solid-state physics, e.g., superconductivity, strength of materials, X-ray diffraction, electrical resistivity, magnetic potential energy, magnetic susceptibility, statics, dynamics, interference, diffraction, and spectrometry. Required in the field of concentration. Prerequisite: PHY 303, 310. Corequisite: PHY 304. Spring semester.

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. Prerequisite: MTH 220. 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. Prerequisite: PHY 202 (PHY 303 is recommended.) Spring, odd-numbered years.

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.) Prerequisites: PHY 304 and 311. Fall, odd-numbered years.

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.) Corequisite: PHY 507. Prerequisites: PHY 304 and 311. Fall, even-numbered years.

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.) Prerequisites: PHY 304 and 311. 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.

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 through the use of mathematical operators. This course is essential for those wishing to pursue graduate study in physics or related areas. Required in the field of concentration. Prerequisites: PHY 304 and PHY 311. Offered each fall.

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: PHY 304 and PHY 490 (or senior standing in physics with instructor's permission.) (One course chosen from PHY 507, 509, 511 or PHY 520 is required for the major.) Fall, even-numbered years.

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.) Prerequisite: PHY 303 and PHY 310 (PHY 304 and PHY 311 are recommended.) Spring, odd-numbered years

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 groundwork in crystal structure, crystal binding energies, crystal diffraction and the reciprocal lattice. We will then consider 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. (One course chosen from PHY 507, 509, 511, or PHY 520 is required for the major.) Prerequisite: PHY 490 and PHY 304. (PHY 421 and 451 are recommended) .Spring, odd-numbered years.