The Bachelor of Science in Mathematics offers a broad background appropriate for students planning to pursue a job in industry, while also offering students the depth and rigor required for graduate studies in mathematics or related fields.
The curriculum satisfies the core Bachelor of Science curriculum that includes certain breadth requirements in mathematics, physics, chemistry, biology, computer science, the humanities and social sciences. In addition to this science core, the student completes twelve upper-level mathematics courses (called technical electives). Most of these technical courses are prescribed by the program but in some cases other courses can be substituted with the approval of the undergraduate advisor. The program includes two general electives which can be applied toward a minor in another discipline.
A recommended study plan is shown below for the standard program in mathematics. These courses do not need to be taken exactly in the order shown and, if these courses do not meet your needs and goals, your program can be changed with the consent of your advisor. For example, you may wish to write a senior thesis, or you may be eligible for Advanced Placement (AP) or the honors calculus sequence. Alternatively, you may want to strengthen your grasp of fundamental concepts by taking MA 134 Discrete Mathematics. The department web page for Undergraduate Courses includes information on when particular courses are offered. See also the comments following the study plan regarding recommended electives and possible course substitutions.
Note that the study plan shown here is for freshmen entering Stevens in fall of 2008. Students that entered Stevens prior to 2008 should consult the appropriate year in the Academic Catalog.
Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants.
Vectors, kinetics, Newton’s laws, dynamics or particles, work and energy, friction, conserverative forces, linear momentum, center-of-mass and relative motion, collisions, angular momentum, static equilibrium, rigid body rotation, Newton’s law of gravity, simple harmonic motion, wave motion and sound.
Atomic structure and periodic properties, stoichiometry, properties of gases, thermochemistry, chemical bond types, intermolecular forces, liquids and solids, chemical kinetics and introduction to organic chemistry and biochemistry.
Laboratory work to accompany CH 115: experiments of atomic spectra, stoichiometric analysis, qualitative analysis, and organic and inorganic syntheses, and kinetics.
This is a first course in computer programming for students with no prior experience. Students will learn the core process of programming: given a problem statement, how does one design an algorithm to solve that particular problem and then implement the algorithm in a computer program? The course will also introduce elementary programming concepts like basic control concepts (such as conditional statements and loops) and a few essential data types (e.g., integers and doubles). Exposure to programming will be through a self-contained user-friendly programming environment, widely used by the scientific and engineering communities, such as Matlab. The course will cover problems from all fields of science, engineering, and business.
Techniques of integration, infinite series and Taylor series, polar coordinates, double integrals, improper integrals, parametric curves, arc length, functions of several variables, partial derivatives, gradients and directional derivatives.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves.
Phase equilibria, properties of solutions, chemical equilibrium, strong and weak acids and bases, buffer solutions and titrations, solubility, thermodynamics, electrochemistry, properties of the elements and nuclear chemistry.
Laboratory work to accompany CH 116: analytical techniques properties of solutions, chemical and phase equilibria, acid-base titrations, thermodynamic properties, electrochemical cells, and properties of chemical elements.
Biological principles and their physical and chemical aspects are explored at the cellular and molecular level. Major emphasis is placed on cell structure, the processes of energy conversion by plant and animal cells, genetics and evolution, and applications to biotechnology.
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
An introduction to experimental measurements and data analysis. Students will learn how to use a variety of measurement techniques, including computer-interfaced experimentation, virtual instrumentation, and computational analysis and presentation. First semester experiments include basic mechanical and electrical measurements, motion and friction, RC circuits, the physical pendulum, and electric field mapping. Second semester experiments include the second order electrical system, geometrical and physical optics and traveling and standing waves.
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition.
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes. Engineering curriculum requirement.
Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model.
An introduction to experimental measurements and data analysis. Students will learn how to use a variety of measurement techniques, including computer-interfaced experimentation, virtual instrumentation, and computational analysis and presentation. First semester experiments include basic mechanical and electrical measurements, motion and friction, RC circuits, the physical pendulum, and electric field mapping. Second semester experiments include the second order electrical system, geometrical and physical optics and traveling and standing waves.
An introduction to statistical inference and to the use of basic statistical tools. Topics include descriptive and inferential statistics; review of point estimation, method of moments, and maximum likelihood; interval estimation and hypothesis testing; simple and multiple linear regression; analysis of variance and design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software is used throughout the course for exploratory data analysis and statistical inference based in examples and in real data relevant for applications.
This course introduces basic concepts and methods in complex analysis. Topics include complex numbers and their properties, followed by limits, continuity, complex differentiation, analytic functions, the Cauchy-Riemann equations, complex integrations, Cauchy's integral formula, Taylor and Laurent series, Cauchy residue theorem, applications of contour integrals, conformal mappings, and applications in physics and engineering.
Seminar in selected topics, such as: combinatorial topology, differential geometry, finite groups, number theory, or statistical techniques. Enrollment limited. Instructor’s permission required. May be taken twice for credit.
Simple harmonic motion, oscillations and pendulums; Fourier analysis; wave properties; wave-particle dualism; the Schrödinger equation and its interpretation; wave functions; the Heisenberg uncertainty principle; quantum mechanical tunneling and application; quantum mechanics of a particle in a "box," the hydrogen atom; electronic spin; properties of many electron atoms; atomic spectra; principles of lasers and applications; electrons in solids; conductors and semiconductors; the n-p junction and the transistor; properties of atomic nuclei; radioactivity; fusion and fission. Spring Semester.
A rigorous introduction to group theory and related areas with applications as time permits. Topics include proof by induction, greatest common divisor, and prime factorization; sets, functions, and relations; definition of groups and examples of other algebraic structures; and permutation groups, Lagrange's Theorem, and Sylow's Theorems. Typical application: error correcting group codes. Sample text: Numbers Groups and Codes, Humphries and Prest, Cambridge U.P.
This course begins with a brief introduction to writing programs in a higher level language, such as Matlab. Students are taught fundamental principles regarding machine representation of numbers, types of computational errors, and propagation of errors. The numerical methods include finding zeros of functions, solving systems of linear equations, interpolation and approximation of functions, numerical integration and differentiation, and solving initial value problems of ordinary differential equations.
This course offers more in-depth coverage of differential equations. Topics include ordinary differential equations as finite-dimensional dynamical systems; vector fields and flows in phase space; existence/uniqueness theorems; invariant manifolds; stability of equilibrium points; bifurcation theory; Poincaré-Bendixson Theorem and chaos in both continuous and discrete dynamical systems; and applications to physics, biology, economics, and engineering.
This course introduces students to the fundamentals of mathematical analysis at an adequate level of rigor. Topics include fundamental mathematical logic and set theory, the real number systems, sequences, limits and completeness, elements of topology, continuity, derivatives and related theorems, Taylor expansions, the Riemann integral, and the Fundamental Theorem of Calculus.
Students will do a research project under the guidance of a faculty advisor. Senior standing and prior approval are required. Topics may be selected from any area of mathematics with the instructor's approval. Each student will be required to present results in both a written and oral report. The written report may be in the form of a senior thesis.
This is an introductory course to number theory. Topics include divisibility, prime numbers and modular arithmetic, arithmetic functions, the sum of divisors and the number of divisors, rational approximation, linear Diophantine equations, congruences, the Chinese Remainder Theorem, quadratic residues, and continued fractions.
This course is an introduction to the geometry of curves and surfaces. Topics include tangent vectors, tangent bundles, directional derivatives, differential forms, Euclidean geometry and calculus on surfaces, Gaussian curvatures, Riemannian geometry, and geodesics.
This course introduces principles of real analysis and the modern treatment of functions of one and several variables. Topics include metric spaces, the Heine-Borel theorem in R-n, Lebesgue measure, measurable functions, Lebesgue and Stieltjes integrals, Fubini's theorem, abstract integration, L-p classes, metric and Banach space properties, and Hilbert space.
Students may choose CS 115, Intro. to Computer Science, in place of CS 105.
(2)
Thermodynamics can be either Ch 321 or E 234.
(3)
Students may choose MA 361, Intermediate PDE, in place of MA 360.
Program Notes:
Students interested in computational aspects of mathematics should plan to take MA 134, CS 115, and CS 284.
Majors entering with AP credit for Calculus I should consider enrolling in the Honors Calculus sequence, MA 182, 281, and 282 in place of MA 116, 221, and 227.
Contact
Yi Li Associate Professor Kidde Room 225 Phone: 201.216.5433 Fax: 201.216.8321 yli6@stevens.edu
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