Applied Mathematics. Dr. Carlos Marques, Chair Mathematics Dept School of Arts & Sciences

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1 Applied Mathematics Dr. Carlos Marques, Chair Mathematics Dept School of Arts & Sciences Bachelor of Science Degree The Applied Mathematics Bachelor of Science program provides a solid background in mathematics and its applications within a highly supportive and stimulating learning environment. Mathematics is the language of Science and Technology. Thus the Applied Mathematics program is at the very heart of the mission of Farmingdale State College. Students benefit from small class size, personal attention, and a network of social and academic opportunities including our Mathematics Club, the Center for Applied Mathematical Sciences, the Mathematics Tutoring Center, and the Undergraduate Teaching Assistant program. Students will acquire strong quantitative and analytic skills, incorporating the use of powerful state-of-the art computational technology in advanced problem solving and research projects. All students will complete a major project in our Seminar in Applied Mathematics which will involve collaborative work. The students have a choice of two tracks within the Bachelor of Science program: the Traditional Track and the Financial Mathematics Track. Both of these tracks share a common core of required General Education courses and of required Mathematics courses. Students in the Traditional Track choose additional elective courses in mathematics and in other fields of their interest, while students in the Financial Mathematics Track must take a set of prescribed courses in financial mathematics and in related fields such as Economics, Business, as well as some elective courses. (See the Program of Study) Students can combine the Bachelor of Sciences in Applied Mathematics (Major) with a Minor in another field, or even obtain a Dual Major in mathematics and a related field. These minors and dual majors enable students to pursue inter-disciplinary interests which enhance future employment opportunities. Applied Mathematics graduates possess the skills to enter a wide variety of excellent careers. An applied mathematics degree provides the background for jobs in business, telecommunications, finance, actuarial science, operations research, transportation, and education. Appropriate elective courses in areas such as computer science, engineering technology, economics, or natural sciences permit students to apply their mathematical knowledge to these fields, opening employment opportunities in additional careers, including pharmaceutical research, information services, and quality control. Applied Mathematics graduates are also well prepared to continue their studies at the graduate level in various fields of applied mathematics, finance, applied sciences, or mathematics education. Typical Employment Opportunities Financial Analyst Economical Analyst Marketing Researcher Actuarial Assistant Statistician

2 Bio Statistician Environmental Mathematician Insurance Manager Secondary Education Teacher Information Consultant Imaging Scientist Quality Control Manager Applied Mathematics (BS) Program Outcomes: Graduates will know the methods and techniques of applied mathematics and will understand the underlying theoretical foundations Graduates will have the knowledge and skills needed to be productive problem solvers and critical thinkers Graduates will possess both depth and breadth in the mathematical sciences Graduates will possess important contextual skills including computer skills, communication skills, and the ability to collaborate with others on mathematical projects. Fall Subject to Revision Liberal Arts and Sciences Courses EGL 101 Composition I: College Writing (GE) 3 EGL 102 Composition II: Writing About Literature 3 Humanities (GE) 3 The Arts (GE) 3 American/Other World/Western Civilization History (GE) 3 Foreign Language (GE) 3 Social and Bahavioral Science (GE) 3 Natural Science (GE) 3 General Education Elective (GE) 3 Liberal Arts and Sciences Elective 3 Required Mathematics Courses for both Tracks MTH 150 Calculus I (GE) 4 MTH 151 Calculus II (GE) 4 MTH 245 Linear Algebra 3 MTH 250 Introduction to Graph Theory and Combinatorics (for Traditional Applied Mathematics Track) OR (30 credits) (40 credits) MTH 246 Introduction to Financial Mathematics (for Financial Mathematics Track) 3

3 MTH 252 Calculus III 4 MTH 253 Differential Equations 4 MTH 290 Methods of Proof in Advanced Mathematics 3 MTH 354 Principles of Real Analysis 3 MTH 360 Applied Probability and Statistics 3 MTH 365 Vector Calculus 3 MTH 405 Seminar in Applied Mathematics 3 BCS 120 Foundations of Computer Programming I 3 Traditional Applied Mathematics Track (51 credits) Math Upper Division Electives 6 Math Related Electives 15 General Electives 15 Upper Division Electives 15 Financial Mathematics Track (51 credits) MTH 346 Continuous-Time Finance 3 MTH 490 Topics in Applied Mathematics 3 (Financial Engineering) BUS 101 Accounting I 3 ECO 380 Econometrics 3 Math Related Elective 12 General Electives 15 Upper Division Electives 12 Total Credits: 121 This program fulfills all Liberal Arts and Sciences requirements. Degree Type: BS Total Required Credits: 121 Course Descriptions EGL 101 Composition I: College Writing (GE) This is the first part of a required sequence in college essay writing. Students learn to view writing as a process that involves generating ideas, formulating and developing a thesis, structuring paragraphs and essays, as well as revising and editing drafts. The focus is on the development of critical and analytical thinking. Students also learn the correct and ethical use of print and electronic sources. At least one research paper is required. A grade of C or higher is a graduation requirement.

4 Note: Students passing a departmental diagnostic exam given on the first day of class will remain in EGL 101; all others will be placed in EGL 097. Prerequisite is any of the following: successful completion of EGL 097; an SAT essay score (taken prior to March 1, 2016) of 7 or higher; an SAT essay score (taken after March 1, 2016) of 5 or higher; on-campus placement testing. Credits: 3 EGL 102 Composition II: Writing About Literature This is the second part of the required introductory English composition sequence. This course builds on writing skills developed in EGL 101, specifically the ability to write analytical and persuasive essays and to use research materials correctly and effectively. Students read selections from different literary genres (poetry, drama, and narrative fiction). Selections from the literature provide the basis for analytical and critical essays that explore the ways writers use works of the imagination to explore human experience. Grade of C or higher is a graduation requirement. Prerequisite(s): EGL 101 Credits: 3 MTH 150 Calculus I (GE) This is the first course of the calculus sequence. Topics include, differentiation of functions of one variable, introduction to integration, application of differentiation and integration. A graphing calculator is required. Note: Students completing this course may not receive credit for MTH 130. Prerequisite(s): MP4 or MTH 117 or 129 Credits: 4 MTH 151 Calculus II (GE) A continuation of the calculus of one variable. Topics include, differentiation and integration of the transcendental functions, integration techniques, polar coordinates and infinite series. Prerequisite(s): MTH 130 or MTH 150 Credits: 4 MTH 245 Linear Algebra A study of the basic properties of vectors and vector spaces; linear transformations and matrices; matrix representations of transformations; characteristic values and characteristic vectors of linear transformations; similarity of matrices, selected applications. Prerequisite(s): MTH 151 or MTH 236 Credits: 3 MTH 250 Introduction to Graph Theory and Combinatorics (for Traditional Applied Mathematics Track) An introductory to graph theory and combinatorial analysis. The emphasis is on problem solving and applications with some attention to theorems and proofs. Topics include Graph Models, Isomorphism, Planar Graphs, Circuits and Graph coloring, Trees, Minimal Spanning Trees, Arrangements and selections, Generating Functions and Inclusion/Exclusion. Prerequisite(s): MTH 150 Corequisite(s): MTH 245 Credits: 3 MTH 246 Introduction to Financial Mathematics (for Financial Mathematics Track) This is a course designed to introduce concepts in financial markets; present and future value calculations of money related to loans, annuities, and bonds. It also introduces simple but basic no-arbitrage derivations of the prices of the most financial contracts that are traded either on exchanges or over-the-counter (stocks, options and forward contracts) in a single and multi-period asset pricing setting. Students will analyze the valuation and hedging of European and American options and general contingent claims in the framework of the classical binomial model of the stock price. Prerequisite(s): MTH 151 or MTH 236 Credits: 3 MTH 252 Calculus III This is the third course of the calculus sequence. It generalizes single variable calculus to multivariable calculus. Functions of several variables are described numerically, graphically and algebraically. Topics include: partial differentiation, multiple integration, vectors and vector fields and line integrals. Prerequisite(s): MTH 151 Credits: 4 MTH 253 Differential Equations

5 This is an introductory course in ordinary Differential Equations designed to develop an understanding of the qualitative behavior of solutions and its relation to the process being modeled. Use of appropriate computer packages forms an integral part of the course. Topics include: first order differential equations and systems, linear systems, applications including electrical circuits and vibrations, introduction to Laplace Transform. Prerequisite(s): MTH 252 Credits: 4 MTH 290 Methods of Proof in Advanced Mathematics MTH 290 is intended to be a bridge course from lower-division mathematics courses to upper-division mathematics. Topics include Logic and Proofs, Set Theory, Relations, Functions (Onto, One-to-One, Sequences as Functions), Cardinality, Introduction to Algebraic Structures, and Introduction to Concepts of Analysis. The focus will be on writing clear and precise proofs. Prerequisite(s): MTH 151 Credits: 3 MTH 354 Principles of Real Analysis Students will be introduced to the foundations of real analysis through a rigorous development of the real number system. This will be followed by a study of limits, continuity, and differentiability of real functions. The Riemann integral and the Fundamental Theorem of Calculus will be developed rigorously. Sequences and series of real functions will also be discussed. Prerequisite(s): MTH 252 and MTH 290 Credits: 3 MTH 360 Applied Probability and Statistics A calculus-based course which studies applications of probability and statistical inference. Use of appropriate computer packages forms an integral part of the course. Topics are chosen from statistical parameters, continuous and discrete random variables, probability distributions, correlation and regression analysis, design of experiments and ANOVA. Prerequisite(s): MTH 151 or MTH 236 Credits: 3 MTH 365 Vector Calculus The course begins with a detailed development of vector algebra in two- and three- dimensions. Also covered will be differentiation and integration of scalar and vector valued functions of vectors. Vector fields will be discussed with particular attention to line and surface integrals. Important vector theorems such as Green's, Stokes' and the divergence theorem and their important applications will be presented. A discussion of the Fourier series and the Fourier integral will complete the course. Prerequisite(s): MTH 245 and MTH 252 Credits: 3 MTH 405 Seminar in Applied Mathematics This is a capstone course for Applied Mathematics students. Students will work on a major project taken from business, industry or government agency. Students will have to present their results both orally and in writing. The completed report must meet a standard that is acceptable to the business community. Students may work in teams or individually. They will report on their progress as part of the seminar. This course may be taken twice for academic credit. Prerequisite(s): MTH 354 Credits: 3 BCS 120 Foundations of Computer Programming I This course introduces the C++ Programming Language as a means of developing structured programs. Students will be taught to develop algorithms using top-down stepwise refinement. Students will be introduced to the concept of Object Oriented programming through the use of pre- defined classes. In addition, students will get a thorough exposure to C++ syntax and debugging techniques. Credits: 3 MTH 346 Continuous-Time Finance This course introduces Brownian motion, Stochastic Calculus, Ito's integral and Ito's formula which are used to derive the Black-Scholes formula in a continuous-time model rather than a limit of discrete-time models as covered in MTH 246. Pricing derivatives on financial securities using Black-Scholes formula will be covered. Prerequisite(s): MTH 246 Credits: 3

6 MTH 490 Topics in Applied Mathematics Lectures in applied mathematics that may introduce topics not covered in the Applied Mathematics curriculum or may expand upon the content of existing courses. These topics vary from year to year, and the specific description of the content of each course will be publicized in advance by the department. Examples of such topics are computational linear algebra, applied optimization, dynamical modeling, financial mathematics, etc. Prerequisite(s): MTH 245 and MTH 252 Credits: 3 BUS 101 Accounting I Fundamental accounting concepts and principles are covered through an understanding of the following topics: accounting as an information system; analyzing a transaction; the accounting cycle; accounting for both service enterprises and merchandising businesses; deferrals and accruals; reversing entries; systems design; accounting for cash, receivables, temporary investments and inventory; payroll accounting. Students apply concepts to the preparation of special journals, subsidiary ledgers, worksheets and financial statements. Credits: 3 ECO 380 Econometrics The course will focus on application of statistics and mathematics to problems of formulating and estimating models of economic behavior. Topics to be covered: Fundamentals of probability and statistics used in economics and applied science. Introduction to central limit theorem and Gauss Markov theorem; Univariate and Multivariate regression using Ordinary Least Square (OLS); Finite and large- sample properties of the classical regression models; Dummy variables and varying parameter models; specification analysis. Prerequisite(s): MTH 110 and 117 or (MTH 129 and ECO 156 or ECO 157) Credits: 3 Admission to Farmingdale State College - State University of New York is based on the qualifications of the applicant without regard to age, sex, marital or military status, race, color, creed, religion, national origin, disability or sexual orientation.