# Applied Mathematics

**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 Learning 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

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

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.

## Contact Information

## Mathematics

Dr. Carlos A. Marques

Whitman Hall, Room 180A

934-420-2182

mathematics@farmingdale.edu

Monday-Friday 8:30am-5:00pm

### Fall 2023

Subject to revision

Liberal Arts and Sciences Courses | (30-31 credits) |
---|---|

EGL 101 Composition I: College Writing (GE) | 3 |

EGL 102 Composition II: Writing About Literature | 3 |

Humanities (GE) | 3 |

The Arts (GE) | 3 |

US History and Civic Engagement/World History and Global Awareness(GE) | 3 |

World Languages (GE) | 3 |

Social Sciences (GE) | 3 |

Natural Sciences and Scientific Reasoning (GE) | 3 |

General Education Elective (GE) | 3 |

MTH 270 Introduction to Mathematical Computing | 3 |

FYE 101 First Year Experience* | 1 |

Required Mathematics Courses for both Tracks | (43 credits) |

MTH 150 Calculus I (GE) | 4 |

MTH 151 Calculus II (GE) | 4 |

MTH 245 Linear Algebra | 3 |

MTH 252 Calculus III | 4 |

MTH 253 Differential Equations | 4 |

MTH 290 Methods of Proof in Advanced Mathematics | 3 |

MTH 326 Mathematical Modeling in Applied Sciences | 3 |

MTH 341 Probability | 3 |

MTH 354 Principles of Real Analysis | 3 |

MTH 365 Vector Calculus | 3 |

MTH 342 Statistial Inference OR | |

MTH 422 Numerical Methods | 3 |

MTH 405 Seminar in Applied Mathematics | 3 |

BCS 120 Foundations of Computer Programming I | 3 |

Traditional Applied Mathematics Track | (48 credits) |
---|---|

MTH 250 Introduction to Graph Theory and Combinatorics | 3 |

Math Upper Division Electives | 6 |

Math Related Electives | 12 |

Technical Electives | 6 |

Upper Division Electives | 21 |

Financial Mathematics Track | (48 credits) |

MTH 246 Introduction to Financial Mathematics | 3 |

MTH 346 Continuous-Time Finance | 3 |

MTH 446 Financial Engineering | 3 |

BUS 101 Accounting I | 3 |

Math Related Electives | 9 |

Technical Electives | 6 |

ECO 380 Econometrics | 3 |

Upper Division Technical Electives | 21 |

*FYE 101 First Year Experience, is required only for first-time full time freshman students beginning in Fall 2023

**Curriculum Summary**

Degree Type: BS

Total Required Credits: 121-122

Please refer to the General Education, Applied Learning, and Writing Intensive requirement
sections of the College Catalog and consult with your advisor to ensure that graduation
requirements are satisfied.

As a part of the SUNY General Education Framework, all first-time full time Freshman
at Farmingdale State College (FSC) beginning Fall 2023, are required to develop knowledge
and skills in Diversity: Equity, Inclusion, and Social Justice (DEISJ). Students will
be able to fulfill this requirement at FSC by taking a specially designated DEISJ
course that has been developed by faculty and approved by the DEISJ Review Board.
DEISJ-approved courses will be developed in accordance with the guiding principles
and criteria outlined below. DEISJ-approved courses may meet other General Education
Knowledge and Skills areas and/or core competencies and thus be dually designated.
DEISJ-approved courses may also earn other special designations such as those for
Applied Learning or Writing Intensive.

**Math Electives **

MTH 315W History of Mathematics (Writing Intensive)

MTH 356 Integrated Topics in Math and Physics

MTH 320 Geometric Structures

MTH 385 Applied Partial Differential Equations

MTH 325 Mathematical Modeling in the Biological Sciences

MTH 390 Methods in Operations Research

MTH 330 Applied Abstract Algebra

MTH 400 Problem Solving Seminar

MTH 331 Introduction to Topology

MTH 422 Numerical Methods

MTH 342 Statistical Inference

MTH 445 Linear Algebra II

MTH 355 Principles of Complex Analysis

MTH 490 Topics in Applied Mathematics

**Technical Electives **

- Any course that is offered in the School of Technology

- Any Physics Course (or course offered by the Physics Department)

- Any Chemistry Course

- Any Biology Course

- Any BCS course (Computer Systems) or CMP course (Computer Science)

- Any approved Business (BUS) course listed below:

BUS 101 Accounting I

BUS 312 Logistics & Supply Chain Management

BUS 102 Accounting II

BUS 327 Risk Management & Insurance

BUS 220 Financial Information Systems

BUS 330 Cost Management Systems

BUS 258 Production Management

BUS 340 Advanced Business Statistics

BUS 271 Intermediate Accounting I

BUS 400 Quality Techniques

BUS 272 Intermediate Accounting II

BUS 401 Quality Management

BUS 273 Cost Accounting

BUS 404 Financial Markets & Institutions

BUS 291 Investments

BUS 409 Strategic Management

BUS 300 Operations Management

BUS 411 Financial Statement Analysis

BUS 306 Project & Contract Management

BUS 421 Advanced Topics in Corporate Finance

BUS 307 Corporate Finance

BUS 470 Advanced Accounting

BUS 310 Principles of Taxation

BUS 471 Auditing

- Any approved Social and Behavioral Sciences course listed below:

ECO 156 Principles of Eco (Macroeconomics)

ECO 410 Public Finance

ECO 157 Principles of Eco (Microeconomics)

ECO 412 Cost-Benefit Analysis

ECO 250 Quantitative Analysis for Economics

ECO 435 Environmental Economics & Policy

ECO 255 Money and Banking

ECO 480 Forecasting

ECO 260 Intermediate Microeconomics

PSY 311 Organizational Behavior

ECO 262 Managerial Economics

PSY 324 Psych Measurement and Assessment

ECO 270 Intermediate Macroeconomics

PSY 330 Organizational Training and Development

ECO 321 Engineering Economics

PSY 331 Industrial/Organizational Psychology

ECO 340 International Trade

PSY 348 Statistics for Psychology

ECO 341 International Finance

PSY 360 Research Methods

ECO 342 Financial Economics

PSY 414 Applied Personnel Psychology

ECO 380 Econometrics

SOC 122 Introductory Sociology

ECO 401 Industrial Organization

**EGL 101 Composition I: College Writing**

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. 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.

**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

**MTH 270 Introduction to Mathematical Computing**

This course is an introduction to computational, experimental, and algorithmic methods using a computer algebra system. Course topics include computational algebra, functional programming, simulation, and visualization. Numerical calculus, analysis of mathematical models and dynamics, basic linear algebra, and other mathematical problem-solving methods will be discussed. At the completion of the course, students will be familiar with a computer algebra system and how to solve mathematical problems by computational methods. Prerequisite(s): MTH 151 with a grade of C or higher or permission of the Mathematics Department

**FYE 101 First Year Experience**

This course is designed to assist new students in acclimating, connecting, and adjusting to the college campus and experience. Through presentations, discussions and group work, students will become familiar with college resources and learn strategies for academic success. Students will also be introduced to the values and ethical principles of the College and encouraged to reflect on their role/responsibilities as college students. Topics include time management, study skills, stress management, goal setting, course and career planning, self-assessment and awareness, and the development of wellness strategies. Note: Students completing FYE 101 may not receive credit for FRX101, FYS 101, or RAM 101. Credits 1 (1.0)

**MTH 150 Calculus I**

This is the first course of the calculus sequence. Topics include limits, continuity, differentiation of functions of one variable, anti-differentiation, introduction to Riemann sums and integration, the fundamental theorem of calculus, and applications of differentiation and integration. Note: Students completing this course may not receive credit for MTH 130. Prerequisite(s): MP4 or MTH 117 or 129

**MTH 151 Calculus II**

A continuation of Calculus I (MTH 150). Topics include, integration of the transcendental functions, various techniques of integration with applications, improper integrals, sequences and series, power series, and Taylor series. Prerequisite(s): MTH 130 or MTH 150

**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

**MTH 252 Calculus III**

This is the third course of the calculus sequence. It generalizes single variable calculus to multivariable calculus. Topics to be covered: polar coordinates and polar curves, vectors and analytical geometry in three dimensions, -functions of several variables, limits and continuity in space, partial and directional derivatives, gradients, multiple integrals in rectangular, polar, spherical, and cylindrical coordinates. Prerequisite(s): MTH 151

**MTH 253 Differential Equations**

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

**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

**MTH 326 Mathematical Modeling in Applied Sciences**

This course will investigate various mathematical models in the applied sciences taken from real life phenomena. Basic notions of abstraction and how to work on real problems at different levels will be introduced in the course. The Models are explored using analytical, computational and graphical tools as appropriate. Models cover but are not limited to examples from Finance, Economics, Ecology, the Environment, Engineering, Biology and Behavioral Sciences. Prerequisite(s): MTH 151 or MTH 236

**MTH 341 Probability**

This course provides a calculus-based introduction to probability theory and its applications. Topics include: probability spaces, conditional probability and independence, discrete and continuous random variables, mathematical expectations, moment generating functions, bivariate distributions, and central limit theorem. Note: Students who take MTH 341 may not receive credit for MTH 360. Prerequisite(s): MTH 151

**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

**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

**MTH 342 Statistical Inference**

This course is an introduction to statistical inference. The overall objective of the course is the development of basic theory and methods for statistical inference. Topics include parameter estimation, interval estimation, hypothesis testing, regression analysis, and experimental design. Prerequisite(s): MTH 341

**MTH 422 Numerical Methods**

This is an introductory elective course for Applied Mathematics students. Topics include solutions of nonlinear equations, interpolation and approximation of functions, numerical differentiation and integration, iterative techniques in Linear Algebra and others. Solutions of problems using computer will be an integral part of this course. Prerequisite(s): MTH 151 and MTH 245

**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

**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. In addition, students will get a thorough exposure to C++ syntax and debugging techniques. Note: Students completing this course may not receive credit for CSC 111

**MTH 250 Graph Theory and Combinatorics**

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

**MTH 246 Introduction to Financial Mathematics**

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

**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

**MTH 446 Financial Engineering**

This course will use advanced mathematical and computational techniques to solve real-world problems in quantitative finance. Topics will include optimal asset-liability matching, yield curve construction, option valuation, hedging and strategies, portfolio analysis, and risk management. Coursework will emphasize the integration of topics from calculus, linear algebra, and probability with financial theory and applications. Students will develop computational skills using application software such as Excel and MATLAB. Prerequisite(s): MTH 346

**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.

**ECO 380 Econometrics**

Students will learn and apply statistical methods used in empirical economic analysis. The course will cover the following topics: the fundamentals of probability and statistics, hypothesis testing, multivariate linear regression using Ordinary Least Squares (OLS), the statistical properties of OLS under less than ideal circumstances, the use of dummy variables, and specification analysis. Prerequisite(s): MTH 110 and (MTH 117 or MTH 129) and (ECO 156 or ECO 157) and Junior level status.