# Mathematics & Physics B.S

## Program Goals

The Mathematic-Physics BS interdisciplinary program provides sufficient groundwork in both mathematics and physics for employment in industry, the commercial sector, or further study in graduate school.

## Learning Objectives

After completing this program, students should have an undstanding of

• fundamental principles of mathematics and their ability to apply these principles in the solution of problems in:
• CALCULUS
Material learned in the usual sequence of elementary calculus courses - differential and integral calculus of one and of several variables - includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equations, and other branches of mathematics
• ALGEBRA
Elementary algebra: basic algebraic techniques and manipulations acquired in high school and used throughout mathematics
Linear algebra: matrix algebra, systems of linear equations, vector spaces, linear transformations, characteristic polynomials, and eigenvalues and eigenvectors
Abstract algebra and number theory: elementary topics from group theory; theory of rings and modules, field theory, and number theory
• SPECIALIZED TOPICS
Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and integrability, and elementary topology of R and Rn
Discrete mathematics: logic, set theory, combinatorics, graph theory, and algorithms
Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis
• fundamental principles of physics and their ability to apply these principles in the solution of problems in:
• CLASSICAL MECHANICS:
(such as kinematics, Newton's laws, work and energy, oscillatory motion, rotational motion about a fixed axis, dynamics of systems of particles, central forces and celestial mechanics, three-dimensional particle dynamics, Lagrangian and Hamiltonian formalism, noninertial reference frames, elementary topics in fluid dynamics)
• ELECTROMAGNETISM:
(such as electrostatics, currents and DC circuits, magnetic fields in free space, Lorentz force, induction, Maxwell's equations and their applications, electromagnetic waves, AC circuits, magnetic and electric fields in matter)
• OPTICS AND WAVE PHENOMENA:
(such as wave properties, superposition, interference, diffraction, geometrical optics, polarization, Doppler effect)
(B4) THERMODYNAMICS AND STATISTICAL MECHANICS:
(such as the laws of thermodynamics, thermodynamic processes, equations of state, ideal gases, kinetic theory, ensembles, statistical concepts and calculation of thermodynamic quantities, thermal expansion and heat transfer)
• QUANTUM MECHANICS:
(such as fundamental concepts, solutions of the Schrödinger equation (including square wells, harmonic oscillators, and hydrogenic atoms), spin, angular momentum, wave function symmetry, elementary perturbation theory)
• ATOMIC PHYSICS:
(such as properties of electrons, Bohr model, energy quantization, atomic structure, atomic spectra, selection rules, black-body radiation, x-rays, atoms in electric and magnetic fields)
• SPECIAL RELATIVITY:
(such as introductory concepts, time dilation, length contraction, simultaneity, energy and momentum, four-vectors and Lorentz transformation, velocity addition)
• SPECIALIZED TOPICS:
Nuclear and Particle physics (e.g., nuclear properties, radioactive decay, fission and fusion, reactions, fundamental properties of elementary particles), Condensed Matter (e.g., crystal structure, x-ray diffraction, thermal properties, electron theory of metals, semiconductors, superconductors)
• Appropriate laboratory skills for the analysis of physical systems. These include data and error analysis, electronics, instrumentation, radiation detection, counting statistics, interaction of charged particles with matter, lasers and optical interferometers, dimensional analysis, fundamental applications of probability and statistics.
• Appropriate oral and written communication skills that enable students to explain their work to people from a wide variety of backgrounds.
• They should have the ability to process and evaluate effectively both theoretical and real-life quantitative data.
• They should be able to communicate using oral, written, or electronic media, and have the teamwork and leadership skills needed to recognize, isolate, and solve mathematical problems.
• They should be committed and open to continuous learning, new ideas, and be able to bring them to bear to help others.
• Specific outcome include:
• Effective numerical computations
• Effective algebraic computations
• Mastery of  basic algebraic concepts
• Understanding of dynamic relationship, graphs, and basic calculus
• Understanding of advanced topics in calculus
• Effective use of linear algebra and ordinary differential equations
• be able to manipulate abstract objects and ideas
• be able to generalize and analyze ideas
• be able to synthesize ideas
• be able to communicate ideas in writing clearly and effectively
• be able to communicate ideas verbally clearly and effectively
• be able to handle unfamiliar concepts and situations
• be able to apply disciplined thinking techniques to new settings
• be able to visualize geometric situations
• be able to translate real-life data into mathematics
• be able to use computing devices to assist discovery and analysis
• be able to approach situations with multiple perspectives
• Exposure to mathematics research