Mathematics & Physics

This course will explore the fundamentals of algebra and its applications, elementary mathematical models, exploration of data both analytically and graphically, basic statistical inference, and mathematics in society. It is designed to fulfill La Roche's core quantitative reasoning component for students in majors without additional math requirements. It is not intended as sufficient preparation for mathematics courses numbered MATH1023 and higher.

This course focuses on the applications of statistics to the health sciences and nursing fields. The major topics are exploratory data analysis (graphical and numerical descriptions of data); data production and its design; basic concepts and properties of probability and probability distributions, including the normal distribution and sampling distributions; statistical inference (inference about a population mean or proportion and about comparing two population means or proportions, chi-square test for goodness of fit, and ANOVA to compare population means). This course is reserved for students in the health-sciences and nursing programs.

A traditional study of pre-calculus mathematics with emphasis on functions and relations. Includes a review of linear and quadratic equations, rational expressions, exponents, radicals and logarithms. Polynomial, exponential, and logarithmic functions are presented together with the conic sections, systems of equations, determinants, the binomial theorem and mathematical induction.

PREREQUISITE: MATH1010 A traditional course in trigonometry including circular measure, trigonometric ratios, the trigonometry of right and obtuse triangles with applications, trigonometric functions and their graphs, inverse trigonometric functions, identities, and trigonometric equations.

PREREQUISITE: MATH1010 This is a transition course from algebra and trigonometry to, and may serve, therefore, as a preparation for, calculus. The topics covered include functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, trigometric functions and analytic trigonometry, polar coordinates and vectors, and the conic sections.

PREREQUISITE: MATH1010 A one-semester course in the differential and integral calculus of functions of a single variable. Emphasis on concepts and the skills of differentiation and integration with applications from Administration, Economics and Managerial Sciences.

PREREQUISITE: MATH1010 The first semester of a three-semester integrated course in the elements of analytic geometry and differential and integral calculus. Included are the concept and applications of the derivative of a function of a single variable, differentiation of polynomials and the trigonometric functions, the chain, product and quotient rules, implicit differentiation, and differentials. Concludes with anti-differentiation, integration, area under graphs of functions and applications.

PREREQUISITE: MATH1032 A continuation of MATH1032 including applications of the definite integral, area, arc length, volumes and surface area, centroids, average value and theorem of the mean for definite integrals. Derivatives and integrals of transcendental functions are followed by techniques of integration, L'Hopital's Rule and indeterminate forms and improper integrals. Also included are conic sections and polar coordinates.

The study of the fundamentals of probability theory with applications to natural and social sciences as well as to mathematics. Discrete and continuous distributions, sampling theory, linear correlation, regression, statistical inference, estimation and analysis of variance are included.

PREREQUISITE: MATH1010 An intensive one semester course in probability and statistics for science and honors students. Various discrete and continues probability distributions will be examined including the binomial, multinomial, Poisson, uniform, exponential, gamma, and normal distributions. Mathematical expectation, moment generating functions, liner combinations or random variable, sampling distributions, point estimations, confidence intervals, hypothesis testing, analysis of variance, regression, correlation and the method of least square will also examined.

PREREQUISITE: MATH1010 This course introduces MIST students to the non-statistical and non-calculus topics in mathematics that are most relevant to their majors. The major topics to be studied include some or all of the following: logic; set theory; relations, with applications to relational algebra and relational calculus; sequences, geometric series, and mathematics of finance; systems of linear equations and matrices; linear programming; probability; and game theory. Excel enhanced by Visual Basic for Applications is used throughout the course.

This course Provides students with the opportunity to meet and feel comfortable with other STEM students thus providing a necessary safety net for undergraduate success. This course will introduce the Peer-Led Team learning approach utilized in the sciences. Students will be exposed to essential tools necessary for a successful undergraduate and postgraduate career including but not limited to: computational math,coding, instrument interface, data analysis, reports, and presentations. Cross-listed with CHEM1090

PREREQUISITE: MATH1010 As in-depth exploration of the applications of various types of mathematics, with an emphasis on problem solving skills. Writing skills are an integral part of this course. The connecting of mathematical ideas with other subject areas will be emphasized. These areas will include: art, biology, chemistry, coding, computers, demographics, fiction, genetics, logic, management, marketing, music, philosophy, physics, politics, psychology, and social planning. The discussion of original source documents will be an integral part of this course.

PREREQUISITE: MATH1010 As in-depth exploration of the applications of various types of mathematics, with an emphasis on problem solving skills. Writing skills are an integral part of this course. The connecting of mathematical ideas with other subject areas will be emphasized. These areas will include: art, biology, chemistry, coding, computers, demographics, fiction, genetics, logic, management, marketing, music, philosophy, physics, politics, psychology, and social planning. The discussion of original source documents will be an integral part of this course. Honors Institute course.

This course develops the student's ability to critically analyze and solve problems, analogies, and work problems. A variety of problem solving techniques and tools are presented, such as chart and diagrams, flow charts, decision tables, and algorithms. Through the use of non-traditional exercises, a combination of techniques will lead to solutions. NOTE: This course may not be used to satisfy the mathematics requirements. Core Course.

PREREQUISITE: MATH1010 An overview of the Euclidian and non-Euclidian geometries required for teaching mathematics, particularly middle school mathematics, focusing on geometrical shapes and their properties, spatial reasoning, geometrical shapes in nature and art, and application of measurements.

PREREQUISITE: MATH1010 A continuation of MATH1033 including a study of vectors, parametric equations, solid analytic geometry and functions of several variables. Includes partial differentiation, total differentials, multiple integrals and surface and line integrals, the theorems of Gauss and Stokes, and infinite series.

PREREQUISITE: MATH2030 A study of first and second order differential equations, infinite series, Laplace transforms and power series together with existence of solution and uniqueness theorems.

PREREQUISITE: MATH1032 A basic course dealing with mathematics applicable to computer science. It provides an introduction to mathematical methods and covers such topics as: enumeration, set theory, mathematical logic, proof techniques, number systems, functions and relations, graphs and digraphs, trees, combinatorics, basic algebraic structures, recurrence relations, Boolean algebra, and analysis of algorithms.

PREREQUISITE: MATH2050 AND CSCI2017 A continuation of MATH1014. Topics to be covered will include some or all of the following: integers and integers Mod n; counting techniques, combinatorics, and discrete probability; graphs, trees, and relations; Boolean algebras; and models of computation such as grammars, finite-state machines, and Turing machines.

A survey of non-calculus mathematics that provides the solid foundation needed by students in business, social sciences, and non-science courses. Topics covered include linear functions, matrix linear programming, probability and statistics, mathematics of finance, Markov chains and decision theory.

PREREQUISITE: MATH1033 This course is intended for students majoring in the natural sciences who are interested in specific applications of Calculus to Chemistry, Biology, Physics and Neuroscience. Possible topics include: applications of root finding, Taylor Polynomials, Taylor Series, differential equations numerical integration, Fourier series, the implicit function theorem, neuronal models.

A study of the properties of integers, the fundamental theorem of arithmetic, congruences, linear diophantine equations, quadratic residues and continued fractions.

A development of the theory of vector spaces from linear equations, matrices and determinants. Topics include linear independence, bases, dimensions, linear mappings, orthogonal reduction, diagonalization of matrices using eigenvectors and eigenvalues.

PREREQUISITE: MATH1033 A self contained course intended for students majoring in the natural sciences who are interested in specific applications of Mathematics to Neuroscience. Topics include: Isopotential Cells, Differential Equations, The Passive Cable, Fourier Series and Transforms, Dendritic Trees, Reduced Single Neuron Models, Probability and Random Variables, Integrate and Fire Models.

PREREQUISITE: MATH1033

PREREQUISITE: MATH2030 A course focusing on the calculus of complex numbers. Topics covered include complex numbers and functions, differentiation and integration with complex variables, complex series, conformal representation and the calculus of residues.

A calculus-based first course in probability and statistics for science and honors students. Various discrete and continuous probability distributions will be examined including the binomial, multinomial, Poisson, uniform, exponential, gamma and normal distributions. Mathematical expectation, moment generating functions, linear combinations of random variables, sampling distributions, point estimation, confidence intervals, hypothesis testing, analysis of variance, regression, correlation and the method of least squares will also be examined.

PREREQUISITE: MATH3040 A detailed study of topics in statistics: comparison of classical and Bavesian methods in conditional probability and estimation of parametrics, non-linear regression, multiple, partial and rank correlation, indices, time series, analyses of variance for two-way classification with and without interaction, design of experiments, reliability and validity of measurements and non-parametric tests.

PREREQUISITE: MATH2031 A survey course in the development of modern mathematics. Beginning with the rudimentary mathematical concepts developed in prehistoric times, mathematics grew sometimes slowly and sometimes rapidly with the insights of various cultures. In this course we trace this development through ancient Mesopotamia and Egypt, classical Greece, Arabic and Hindu cultures of the Dark and Middle Ages, the European Renaissance and on into the modern times. Special attention will be paid to major developments such as the emergence of mathematics as an organized, reasoned and independent discipline in Classical Greece; the emergence and development of major areas of mathematics such as of algebra, trigonometry, productive geometry, calculus, analytic geometry infinite series, non-Euclidean geometry; and how developments in mathematical thought have shaped the modern world.

PREREQUISITE: MATH2030 An introduction to algebraic concepts such as groups, rings, integral domains and fields. The elementary number systems occupy a central place. Mappings, especially homorphisms, are introduced early and emphasized through out the course.

PREREQUISITE: MATH2030 An overview of geometry in the light of modern trends with attention to axiomatic structure, including an introduction to hyperbolic and elliptic figures as geometric structures together with an overview of projective geometry.

PREREQUISITE: MATH2031 An introductory to classical (real) analysis. Includes a rigorous treatment of logic, set theory, functions, countable and uncountable sets, the real number system, metric spaces, sequences, series, differentiation and integration.

A first course in data reduction and error analysis with emphasis placed more upon hands-on experience than upon theory. Topics covered will include: sample statistics; the Binomial, Poisson, Gaussian and Lorentzian distributions; analysis of the propagation of errors; linear and nonlinear least squares; multiple regression and data manipulation techniques. Students will be expected to perform analyses using commercially available software and software of their own composition.

A practical experience in a field setting.

The Mathematics Capstone is a culminating experience for senior mathematics majors. Students will integrate and apply ideas from across the mathematics curriculum through independent and collaborative projects. Emphasis is placed on problem-solving, research, and the clear communication of mathematical ideas in both written and oral form. The course provides an opportunity for students to demonstrate mastery of their mathematical knowledge and to prepare for professional or graduate pathways.

An individual investigation in the student's field of interest carried out under the supervision of a faculty member. The student is responsible for defining a problem, planning a course of investigation, and reporting higher results in a scientific paper.�

Independent study is an accelerated program for superior students in the division of natural and mathematical sciences. It is intended to allow a student to pursue studies in advanced topics. The student designs an independent study in conjunction with a divisional faculty member. To be eligible for independent study the student must comply with all appropriate college policies.

PREREQUISITE: MATH2031 A survey of numerical techniques for numerically solving a variety of mathematical problems with an emphasis on application as opposed to theory. Topics to be covered include: sources of error in numerical computations, solving nonlinear equations, solving sets of simultaneous equations, interpolating polynomials, numerical integration and numerical differentiation.

PREREQUISITE: MATH4060 Second semester of a survey course in numerical techniques for the numerical solution of a variety of mathematical problems with an emphasis on application as opposed to theory. Topics to be covered include: initial-value problems, partial differential equations, curve fitting and approximation of functions.

The weekly one-hour seminar treats of a topic or of topics important in applied and/or theoretical mathematics. The specific topic or topics may vary from year to year. Topics in the past have included actuarial mathematics, the Millennium Problems, and the Riemann Hypothesis.

An individual investigation in the student's field of interest carried out under the supervision of a faculty member. The student is responsible for defining a problem, planning a course of investigation, and reporting higher results in a scientific paper.

This course is designed for anyone interested in experiencing first-hand the process of the scientific inquiry and modern concepts of physics. In this process students and the professor will pose investigable questions about some physical phenomena which you observe every day. Students will then observe and/or conducts hand-on experiments to develop an understanding of these physical concepts. Each student will report what he/she learned from the class. (SLSC)

PREREQUISITE: MATH1010 This course is designed to provide a broad background in physics for those who will enter the allied health professions. Applications will be made to the biological and physiological sciences, as well as to the various types of equipment. Lecture and laboratory course.

Laboratory for PHYS1010 Physics for Health Science

PREREQUISITE: MATH1032 This is the first of a three-semester introduction to calculus-based physics stressing experimental and problem-solving techniques. Concepts covered are mechanics, kinematics, Newton’s laws of motion, conservation laws, rotational motion, gravitation, oscillation, and wave/acoustics.

PREREQUISITE: MATH1032 Laboratory for PHYS1032 General Physics I

PREREQUISITE: PHYS1032 The second of a three-semester introduction to calculus-based physics. Concepts covered are thermal properties and electromagnetism: thermo dynamics, electricity, magnetism, electromagnetic wave, geometrical optics, and physics optics.

Laboratory for PHYS1033 General Physics II

PREREQUISITE: PHYS1033 The third of a three-semester introduction to calculus-based physics. This course is devoted to the study of the two great theories that underlie almost all of modern physics, quantum theory and relativity theory. There is an emphasis on quantum mechanical description of semiconductor physics, which forms our modern electronics age (computers and electronic communication devices in general). A series of laboratory projects enables the student to retrace experimentally the development of modern physics.

PREREQUISITE: PHYS1033L Laboratory for PHYS2030 General Physics III

An introductory course of electronics. Students will learn the fundamental principles of electronics circuits while engaging in various laboratory projects using electronic components such as passive devices and integrated circuit chips. Topics to be studied include basic circuit theory, diode applications, Bipolar and Filed Effect transistors, operational amplifiers, and basic TTL gates. This course will provide students with both theoretical and practical knowledge necessary to start understanding of computers and data communication devices.

Lab for PHYS2080 Analog Electronics

This course will focus on analyzing problems of physics with numerical methods and simulation techniques. Various problems are selected from Classical Mechanics, Electromagnetism, Thermal/Statistical Physics, and Quantum Mechanics. It will provide students with additional computational skill and knowledge necessary for analyzing various models and simulations of physics and other disciplines.

This is an intermediate digital electronics and focuses on the study of computer architecture, and digital signal processing technology. It will provide students with the working knowledge necessary for understanding in computer science and telecommunication technologies. Students will learn practical digital circuits while conducting practical laboratory projects. Typical digital integrated circuits and digital/analog interface chips will be used for designing and constructing a prototype computer, interfaces, and digital signal processing circuits.

Lab for PHYS3080 Digital Electronics

This course will present the fundamental technology of wireless and cable telecommunications. Students will become familiar with modulation/demodulation and noise reduction for high-fidelity electronic and data communications. They will also learn advanced data communication technologies such as digital broadband technology. Transition from electronics (application of electrons) to photonics (application of lights and photons) is also presented. Hands-on laboratory projects will be conducted in connection with the basic hardware of telecommunication not covered in PHYS2080 Analog Electronics and PHYS 3080 Digital Electronics.

Lab for PHYS3082 Electronic Communication

This course will offer fundamental concepts of physics that forms information and computation theories. The first part of this course is an overview of information theory. The concept of entropy and negative entropy in Thermodynamics and Information will be discussed. Then, noise in electric communication will be treated as a stochastic process. The second part of this course is an introduction to quantum computation and information. Mathematical background of quantum mechanics will be overviewed for the theoretical background of quantum computation/information. Experimental feasibility will be also discussed with recent development. It will provide students with fundamental knowledge of classical and quantum computation/information.

In this course, students will learn how to design and construct test and measurement instruments. They will design, construct various hands-on apparatuses and conduct measurements with their own instruments in the laboratory session. Students will also learn basic knowledge of design and construction of computer-based data acquisition systems and virtual instruments, emphasizing the application of microelectronics for controlling processes and systems. The integration of microprocessors with sensors/actuators and the use of digital device interface are central to these applications. In addition, typical computer network application of laboratory will be overviewed.

Design, construct various hands-on apparatuses and conduct measurements with their own instruments in the laboratory session