The Common Core presents a coordinated, common foundation essential to the education of all students. It includes four semesters of mathematics, three semesters of physics and associated laboratories, two semesters of chemistry and associated laboratories, one writing-intensive course in humanities and social sciences, and one course each in biology, computer science, and engineering.
Core courses address three objectives: (1) acquisition of disciplinary knowledge and experience with disciplinary-related techniques, (2) skill development in the areas of oral and written communication, critical thinking, teamwork and collaboration, project management and/or leadership, and (3) explorations of either the interrelationship of technical work and society or the understanding of one's own culture or other contemporary cultures.
All core courses must be attempted by the end of the fifth semester.
Core courses are listed below. Course descriptions are given in the course listings for the departments.
52. Introduction to Biology. 3 credit hours. Topics in cell biology, molecular biology, genetics, and evolution. Prerequisites: one semester of general chemistry and one semester of calculus.
21-22. General Chemistry. 3 credit hours per semester. Stoichiometry, kinetic theory, phase behavior, equilibrium, bonding, thermodynamics, kinetics and descriptive chemistry.
25-26. Chemistry Laboratory. 1 credit hour per semester. Laboratory taken concurrently with Chemistry 21-22.
5. Introduction to Computer Science. 3 credit hours. Introduction to elements of computer science. Students learn general computational problem-solving techniques and gain experience with the design, implementation, testing and documentation of programs in a high-level language. In addition, students learn to design digital devices, understand how computers work, and learn to program a computer in its own machine language. Finally, students are exposed to ideas in computability theory. The course includes discussions of societal and ethical issues related to computer science.
59. Introduction to Engineering Systems. 3 credit hours. An introduction to the concepts of modern engineering emphasizing modeling, analysis, synthesis and design. Applications to chemical, mechanical and electrical systems. Prerequisites: sophomore standing and concurrent registration in Physics 51.
Humanities and Social Sciences
1. Introduction to the Humanities and Social Sciences. 4 credit hours. An introduction to college level studies in the humanities and social sciences focusing on the development of essential reading, critical thinking, research and especially writing skills.
11. Calculus of One Real or Complex Variable. 2 credit hours. Complex numbers, limits, formal epsilon-delta limit definition, derivatives and differentiation rules; proofs by contradiction and induction; infinite series; integration; applications of the calculus; introduction to calculus of complex-valued functions. Prerequisite: one year of calculus at the high school level.
12. Introduction to Linear Algebra and Discrete Dynamical Systems. 2 credit hours. Matrix representation of systems of equations, matrix operations, determinants; linear independence and dependence, bases; inner products, eigenvalues and eigenvectors; examples of discrete dynamical systems, fixed points, chaos, stability, bifurcations. Prerequisite: Math 11 or the equivalent.
13. Differential Equations I. 1.5 credit hours. Modeling physical systems, first-order ordinary differential equations, existence; uniqueness and long-term behavior of solutions; bifurcations, approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations. Prerequisite: Math 11 or the equivalent.
14. Multivariable Calculus I. 1.5 credit hours. Vectors, dot and cross products; vector descriptions of lines and planes; partial derivatives and differentiability; gradients and directional derivatives; chain rule; higher order derivatives and Taylor approximations; double and triple integrals in rectangular and other coordinate systems; line integrals; vector fields, curl and divergence; introduction to Green's theorem, divergence theorem and Stoke's theorem. Prerequisite: Math 11.
61. Multivariable Calculus II. 1.5 credit hours. Review of basic multivariable calculus; optimization and the Second Derivative Test; constrained optimization using Lagrange multipliers; conservative and nonconservative vector fields; Green's theorem; parametrized surfaces and surface integrals; divergence theorem, outline of proof and applications; Stoke's theorem, outline of proof and applications; unification of major vector theorems. Prerequisite: Math 14.
62. Introduction to Probability and Statistics. 1.5 credit hours. Sample spaces, events, axioms for probabilities; conditional probabilities and Bayes' theorem; random variables and their distributions, discrete and continuous; expected values, means and variances; covariance and correlation; law of large numbers and central limit theorem; point and interval estimation; hypothesis testing; chi-square goodness of fit; simple linear regression; introduction to analysis of variance; applications to analyzing real data sets. Prerequisite: Math 11.
63. Linear Algebra II. 1.5 credit hours. Review of basic linear algebra; vector spaces; row and column spaces of matrices, rank-nullity theorem; orthogonal bases and Gram-Schmidt procedure; orthogonal expansion and Fourier coefficients; linear transformations; change of basis and similarity; eigenvalues, eigenvectors and characteristic polynomials; diagonalization of symmetric matrices; applications of eigenvalues to systems of ordinary differential equations. Prerequisite: Math 12.
64. Differential Equations II. 1.5 credit hours. Review of basic ordinary differential equations, especially systems; undriven linear systems; orbital portraits; stability and conservative systems; Lyapunov functions; cycles and long-term behavior of solutions; Sturm-Liouville problems; series solutions near ordinary and regular singular points; Bessel functions; chaos. Prerequisite: Math 13 and Math 63.
23. Special Relativity and an Introduction to Quantum Mechanics. 2 credit hours. Time dilation, length contraction, Lorentz transformations, spacetime, relativistic momentum and energy; the wave and particle nature of light, the principles of quantum mechanics as seen in the sum-over-paths approach to the subject.
24. Mechanics and Wave Motion. 3 credit hours. Kinematics, dynamics, linear and angular momentum, work and energy, harmonic motion, waves and sound.
28. Physics Laboratory. 1 credit hour. Experiments in mechanics using digital electronic measuring devices. Corequisite with Physics 24.
51. Electromagnetic Theory and Optics. 3 credit hours. An introduction to electricity and magnetism leading to Maxwell's electromagnetic equations in differential and integral form. Selected topics in physical optics. Prerequisites: Physics 23-24 and Mathematics 14.
53. Electricity and Optics Laboratory. 1 credit hour. Electrical and magnetic techniques in such measurements as the Hall effect and the earth's magnetic field. Introduction to electronics, including use of the oscilloscope and measurements on RC and RCL circuits. Experiments in physical optics, including studies of diffraction patterns. Prerequisite: Physics 51 or concurrently.
Getting through the Common Core
For many students the academic program in the first two years consists of the Common Core, two additional humanities or social sciences courses, two courses in the major and two electives. Usually it is possible for students to delay their choice of a major until midway through the sophomore year or even to the beginning of the junior year. Students should consult their academic advisors early in their program in order to ensure that their options will remain open. After the first year, students must register for all deficient first-year courses each time they are offered. All such courses must be passed before the beginning of the junior year. Sample programs for the first two years appear below.
|Sample First-Year Program||First Semester Credit Hours||Second Semester Credit Hours|
|Chemistry 21/22, 25/26 General Chemistry with Lab||4||4|
|Computer Science 5||3|
|Introduction to Computer Science|
|Humanities and Social Sciences 1,||4||3|
|Introduction to Humanities and Social Sciences/Fall|
|Mathematics 11-12 & 13-14||4||3|
|Calculus of One Variable|
|Linear Algebra I|
|Differential Equations I|
|Multivariable Calculus I|
|Physics 23-24, 28||2||4|
|Special Relativity and an Introduction
to Quantum Mechanics
|Mechanics and Wave Motion with Lab|
|Introduction to Biology|
|Approved PE course|
|TOTAL||17 hours||17 hours|
The instructors in the first-year program meet regularly with the Associate Dean for Academic Affairs to insure that course material, major assignments and examinations are coordinated throughout the year.
|Sample Sophomore Program
|Introduction to Engineering Systems
|Mathematics 61, 62, 63, 64
|Multivariable Calculus II
|Introduction to Probability & Statistics
|Linear Algebra II
|Differential Equations II
|Physics 51, 53
|Electromagnetic Theory & Optics with Lab
|Introduction to Biology or an elective
|Humanities and Social Sciences