# 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. 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. Students can also enroll in one or more of the following microcredentials while satisfying the requirements for the major or minor and/or advancing their career.

- Computational Mathematics
- Data Analytics
- Financial Mathematics

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. Worku T. Bitew

Whitman Hall, Room 180A

934-420-2182

mathematics@farmingdale.edu

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

### Fall 2024

Subject to revision

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

FYE 101 First Year Experience (required of first-time freshmen only) | 1 |

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

EGL 102 Composition II: Writing About Literature | 3 |

Humanities (GER) | 3 |

The Arts (GER) | 3 |

World History and Global Awareness OR US History and Civic Engagement (GER) | 3 |

World Languages (GER) | 3 |

Social Sciences (GER) | 3 |

Natural Sciences and Scientific Reasoning (GER) | 3 |

Oral Communication (GER) | 3 |

BCS 109 Introduction to Programming OR CSC 111 Computer Programming I | 3 |

Mathematics Courses | (52 credits) |

MTH 150 Calculus I (GER) | 4 |

MTH 151 Calculus II (GER) | 4 |

MTH 245 Linear Algebra | 3 |

MTH 246 Introduction to Financial Mathematics | 3 |

MTH 252 Calculus III | 4 |

MTH 253 Differential Equations | 4 |

MTH 270 Introduction to Mathematical Computing | 3 |

MTH 290 Methods of Proof in Advanced Mathematics | 3 |

MTH 326 Mathematical Modeling in Applied Sciences (AL) | 3 |

MTH 354 Principles of Real Analysis | 3 |

MTH 360 Applied Probability and Statistics | 3 |

MTH 405 Seminar in Applied Mathematics | 3 |

Math Upper Division Electives | 12 |

Math Related Electives | 12 |

Upper Division Electives (2) | 21 |

General Electives (1) | 6 |

Program Total Credits | 121-122 |

**Curriculum Summary**

Degree Type: BS

Total Required Credits: 121-122

1. General Electives: Any SUBJ 100 or higher level (except MTH 322) AND no more than
3 credits in PED. If the DEIS requirement is not satisfied through dual designation
in another GER course, one of the approved DEIS courses must be selected as one of
the two General Electives.

2. Upper Division Electives: Any SUBJ 300 or higher level (except MTH 322).

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 Upper Division Electives **

- MTH 315W History of Mathematics (Writing Intensive)
- MTH 320 Geometric Structures
- MTH 325 Mathematical Modeling in the Biological Sciences
- MTH 330 Applied Abstract Algebra
- MTH 331 Introduction to Topology
- MTH 341 Probability
- MTH 342 Statistical Inference
- MTH 346: Quantitative Finance
- MTH 355 Principles of Complex Analysis
- MTH 356 Integrated Topics in Math and Physics
- MTH 365 Vector Calculus
- MTH 380: Experimental Design
- MTH 385 Applied Partial Differential Equations
- MTH 390 Methods in Operations Research
- MTH 400 Problem Solving Seminar
- MTH 420: Statistical Data Mining
- MTH 422 Numerical Methods
- MTH 445 Linear Algebra II
- MTH 446 Financial Engineering
- MTH 460 Applied Probability and Statistcs II
- MTH 490 Topis in Applied Mathematics

**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)

**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

**BCS 109 Introduction to Programming**

Using Python, this course covers the basic concepts of computer programming. Python is an easy-to learn, high-level computer programming language that is widely used in many applications. This course introduces the fundamental elements of programming such as expressions, conditionals, loops, functions, files, and then use these elements to create simple interactive applications. This course covers also simple GUI and animation-based applications.

**CSC 111 Computer Programming I**

This is an introductory programming course. Students will be taught basic concepts of computer programming and problem solving using an object-oriented language. Selection, repetition, methods, classes, and arrays will be covered. Note: CSC 101 is recommended as a prerequisite, but not required for this course. Note: Students completing this course may not receive credit for BCS 120.

**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 246 Introduction to Financial Mathematics**

This is a course designed to introduce the basic concepts of financial mathematics including cashflows, the time value of money, compounding, and present and future value calculations for loans, annuities, and bonds. The course presents the basic no-arbitrage principal to derive forward interest rates and stock prices as well as the prices of futures contracts. Students will be introduced to options, their characteristics, and put-call parity and will analyze the valuation of calls and puts, and general contingent claims, in the framework of the classical one-period binomial model. Prerequisite(s): MTH 130 or MTH 150

**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 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, 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 130 or MTH 150

**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 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 360 Applied Probability and Statistics**

In this course, we study applications of probability distributions and statistical inference. Topics are chosen from statistical parameters, continuous and discrete random variables, probability and sampling distributions, confidence intervals, hypothesis testing, regression analysis, and analysis of variance. Prerequisite(s): MTH 130 or MTH 150

**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

**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 346 Quantitative Finance**

This course introduces more advanced topics in financial mathematics. Multi-period, discrete-time asset pricing will be presented within the framework of the classic binomial tree model and it's application to pricing and hedging contingent claims, such as stock options and callable bonds, will be analyzed. The Black-Scholes option pricing formula will be presented and it's relationship to the discrete-time model will be explored. Option and bond risk-factors, such as delta/gamma and duration/convexity, will be introduced. Finally, mean-variance portfolio analysis will be presented, including the efficient frontier and optimal asset allocation. Throughout the course, students will gain insight via lab-projects to gain real-world experience in quantitative finance. 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 Financial Accounting**

Students will study the underlying framework of financial accounting systems and apply these concepts in preparing, interpreting and analyzing accounting information in the contemporary corporate business environment. Students will record business transactions, and prepare and analyze financial statements for service and merchandising companies. Students will demonstrate an understanding of accounting systems and controls, financial assets, plant assets, current and long-term liabilities, and equity.

**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 or BUS 240 or MTH 341) and (ECO 156 or ECO 157) and (MTH 116 or MTH 117 or MTH 129) and Junior level status.