May 13, 2024  
2021-2022 Undergraduate Academic Catalog and Student Handbook 
    
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2021-2022 Undergraduate Academic Catalog and Student Handbook [ARCHIVED CATALOG]

Department of Applied Mathematics

Applied Mathematics

Department Chair: Dr. Michael Brilleslyper, Professor, Mathematics

 

Degree Programs

Applied Mathematics

Overview

The Department of Applied Mathematics offers a Bachelor of Science degree in Applied Mathematics.  In addition, the department offers foundational and advanced coursework that supports all the STEM programs at Florida Poly.  The program in applied mathematics covers a breadth of mathematical topics, as well as an interdisciplinary sequence in another STEM field.  The degree program is flexible and develops the analytical, theoretical, and technical skills needed for high tech jobs, as well as for further study in graduate school in a variety of disciplines.

Bachelor of Science, Applied Mathematics

See Program Description  for full curriculum and additional details.

Florida Common Prerequisites

Students who started as freshmen at FPU (native students) must complete general education requirements and the following courses to enter the degree program as a junior:

  • COP 2271C - Introduction to Computation and Programming Credits: 3
  • MAC 2311 - Analytic Geometry and Calculus 1 Credits: 3
  • MAC 2312 - Analytic Geometry and Calculus 2 Credits: 3
  • MAC 2313 - Analytic Geometry and Calculus 3 Credits: 3
  • MAP 2302 - Differential Equations Credits: 3

Any of the following:

  • BSC 1010/1010 L - Biology 1 and Biology 1 Laboratory Credits: 4
  • CHM 2045/2045 L - Chemistry 1 and Chemistry 1 Laboratory Credits: 4
  • PHY 2048/2048L - Physics 1 and Physics 1 Laboratory Credits: 4

Transfer students must meet general education requirements and satisfy the following Florida State Common Prerequisites to enter the degree program as a junior:

COP XXXX

& MAC X311

& MAC X312

& MAC X313

& BSC XXXX/XXXXL

  • or CHM XXXX/XXXXL

  • or PHY XXXX/XXXXL

  • or GLY XXXX/XXXXL

& MAP X302

Students are strongly encouraged to select required lower division electives that will enhance their general education coursework and that will support their intended baccalaureate degree program. Students should consult with an academic advisor in their major degree area.
——————————–

  1.  a scientific programming course designed for computer science majors
  2.  one laboratory based science course designed for science majors

NOTE that all universities require a ‘C’ grade or better for admission.

 Academic Learning Compact

Florida Polytechnic University’s Academic Learning Compact describes what students, who follow the major’s study plan, will know and be able to do. These are listed as core student learning outcomes.

College

Engineering

Program

Applied Mathematics

Purpose of the Program:

The Applied Mathematics Bachelor of Science degree at Florida Polytechnic University provides a broad education in mathematics with a focus on applications to other STEM fields, such as engineering, physics, and computer science. The program requires a four-course sequence in another discipline where mathematics plays a significant role. Students in the program acquire an in-depth understanding of the mathematical concepts, principals, and theory that underpin all STEM fields. Applied mathematics students use a broad range of techniques, to include modeling, computation, and data analysis, in solving complex problems and providing innovative solutions.

Graduates of the program will demonstrate the following:

Graduates of the Applied Mathematics program will demonstrate the following:

 

  1. An ability to identify, formulate, analyze, and solve complex problems involving mathematics and scientific reasoning
  2. An ability to explain complex ideas and communicate effectively with a range of audiences
  3. An ability to use data, experimentation, and the scientific method to draw and defend conclusions
  4. An ability to function effectively on interdisciplinary in a collaborative and inclusive environment
  5. An ability to independently acquire and apply new knowledge as needed
  6. An ability to produce best solutions that meet specified needs, while considering public health, safety, and welfare, as well as global, cultural, environmental, and economic factors
  7. An ability to recognize ethical and professional responsibilities in scientific work and make informed judgments, while considering the impact of proposed solutions in global, economic, environmental, and societal contexts

 

 

Core Learning Outcomes:

Student Learning Outcomes

The Outcomes Involve These Skills:

Upon completion of the Applied Mathematics Degree, students will possess:

Content

Critical Thinking

Communication

An ability to identify, formulate, analyze, and solve complex problems involving mathematics and scientific reasoning

X

X

 

An ability to explain complex ideas and communicate effectively with a range of audiences

 

 

X

An ability to use data, experimentation, and the scientific method to draw and defend conclusions

 

X

 

An ability to function effectively on interdisciplinary in a collaborative and inclusive environment

X

 

X

An ability to produce best solutions that meet specified needs, while considering public health, safety, and welfare, as well as global, cultural, environmental, and economic factors

X

X

 

An ability to recognize ethical and professional responsibilities in scientific work and make informed judgments, while considering the impact of proposed solutions in global, economic, environmental, and societal contexts

 

X

 

Course Offerings

Courses

  • BME 4422 - The Biophysics of Neural Computation

    Credits: 3

    Prerequisites: MAP 4484 - Mathematical Modeling in Biology I  
    Course Description:  

    This course will discuss the biophysics of neuronal computation for both biological and artificial neural networks. It will provide a detailed introduction to: i) the anatomy/physiology of excitable cells, ii) the major brain architectures and principles, and iii) the most relevant mathematical models for neural computation from single neurons to circuits. Therefore, this course will prepare the students to understand the main principles by means of which our brains work and computers recognize patterns, learn/plan actions, and interact with humans

  • EEL 4822 - Pattern Recognition

    Credits: 3

    Prerequisites: MTG 4930
    Course Description: The main goal of this course is to underlie the principles of pattern recognition and the methods of machine intelligence used to develop and deploy pattern recognition applications in the real world. The algorithms to be presented include feature extraction and selection, clustering, artificial neural networks, support vector machines, rule-based algorithms, fuzzy logic, genetic algorithms, and others. Case studies drawn from actual machine intelligence applications will be used to illustrate how methods such as pattern detection and classification, signal taxonomy, machine vision, anomaly detection, data mining, and data fusion are applied in realistic problem environments. 

  • EGS 3441 - Engineering Statistics

    Credits: 3

    Prerequisites: MAC 2311 - Analytic Geometry and Calculus 1  with a minimum grade of a C
    Course Description: The basic concepts in probability and statistics with engineering applications. Topics include probability, discrete and continuous random variables, estimation, hypothesis testing, and linear and multiple regression.

  • ISC 4420 - Introduction to Bioinformatics

    Credits: 3

    Prerequisites: BSC 1010 - Biology 1  and COP 2271C - Introduction to Computation and Programming  
    Course Description: This is an introduction to the theory and practice of Bioinformatics and Computational Biology; Emphasizing the use of computer databases to store, retrieve and assist in understanding Biological Information.

    Topics covered will included:

    1. DNA Sequence Assembly and Patterns

    2. Protein Modeling and Alignments

    3. Genomics and Proteomics

    4. Expression Array Analysis

    5. Phylogenetics and Systematics   

  • ISC 4930 - Special Topics -Applied Studies

    Credits: 3

    Prerequisites: Consent of department head and instructor
    Course Description: This course investigates a topic of special interest to faculty and students that is outside regular course offerings.

  • MAA 4102 - Introduction to Advanced Calculus for Engineers and Physical Scientists

    Credits: 3

    Prerequisites: MAC 2313 - Analytic Geometry and Calculus 3  and (MAS 3105 - Linear Algebra  or MAS 3114 - Computational Linear Algebra  )
    Course Description:  

    Theory of real numbers, functions of one variable, sequences, limits, continuity and differentiation; continuity and differentiability of functions of several variables.

  • MAA 4402 - Complex Variables

    Credits: 3

    Prerequisites: MAC 2313 Analytic Geometry and Calculus 3  
    Course Description: This course covers the algebra of complex numbers, analytic and harmonic functions, Cauchy-Riemann conditions; complex integration, Cauchy’s Theorem and integral formual; power series; and applications to engineering and physics. 

    (Amended 10/25/2021; New Course Offering)
    Primary Term(s) Offered: Rotation Year

  • MAC 1147 - Pre-calculus Algebra and Trigonometry

    Credits: 4

    Prerequisites: None
    Course Description: Topics include the study of polynomial, rational, absolute value, exponential, and logarithmic functions. Other topics include matrices, system of equations and inequalities, Trigonometric functions and applications, analytic trigonometry. This course is intended for students whose major requires the calculus sequence.

  • MAC 2311 - Analytic Geometry and Calculus 1

    Credits: 4

    Prerequisites: Any of the following:

    a grade of C in a MAC course numbered 1147 or higher

    IB credit for a MAC course numbered 1147 or higher.

    Any course grades, AP or IB scores used to meet this prerequisite must be on file by registration.
    Course Description: This course is an introduction to analytic geometry; limits; continuity; differentiation of algebraic, trigonometric, exponential and logarithmic functions; applications of the derivative; inverse trigonometric functions; differentials; introduction to integration; and the fundamental theorem of calculus.

  • MAC 2312 - Analytic Geometry and Calculus 2

    Credits: 4

    Prerequisites: MAC 2311 - Analytic Geometry and Calculus 1  
    Course Description: Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential, and logarithmic functions; sequences and series are presented in this class.

  • MAC 2313 - Analytic Geometry and Calculus 3

    Credits: 4

    Prerequisites: Letter grade of C or better in MAC 2312 - Analytic Geometry and Calculus 2  (Amended 10/25/2021)
    Course Description: This course covers solid analytic geometry, vectors, partial derivatives and multiple integrals.

  • MAD 2104 - Discrete Mathematics

    Credits: 3

    Prerequisites: MAC 2312 - Analytic Geometry and Calculus 2  
    Course Description: This course discusses logic, sets, functions, integers, mathematical reasoning and induction, counting principles, permutations and combinations, discrete probability, advanced counting techniques and inclusion-exclusion.

  • MAD 3105 - Discrete Mathematics II

    Credits: 3

    Prerequisites: MAD 2104 - Discrete Mathematics  
    Course Description: The purpose of this course is to develop knowledge and skills in fundamental mathematical topics that are relevant to computing, particularly to the systematic development of software. This course is intended for computer science majors and other science majors with an interest in mathematics. The topics covered in this course include graphs, relations and Boolean Algebra.

  • MAD 3401 - Numerical Analysis

    Credits: 3

    Prerequisites: MAS 3105 - Linear Algebra  or  MAS 3114 - Computational Linear Algebra   
    Course Description: This course introduces students to the development, application, and examination of basic numerical algorithms.

  • MAP 2302 - Differential Equations

    Credits: 3

    Prerequisites: MAC 2312 - Analytic Geometry and Calculus 2  (with a minimum grade of C)
    Course Description: The relationship between differential equations and initial conditions to physical problems in engineering, physics, technology and other applied areas is discussed. Students will be able to formulate, solve, and analyze the results of mathematical models of elementary physical problems and apply them. Topics include: first-order ordinary differential equations, theory of linear ordinary differential equations, solution of linear ordinary differential equations with constant coefficients, the Laplace transform and its application to solving linear ordinary differential equations.

  • MAP 3253 - Mathematical Scientific Computation

    Credits: 3

    Prerequisites: COP 2271 - Introduction to Computation and Programming  and MAP 2302 - Differential Equations  
    Course Description:  

    The mathematical and scientific computation is an interplay between mathematical theory and modern computational tools for applications. Students will attain an advanced knowledge of computer science, specifically programming and will gain a solid foundation in mathematics that will enable them to model or analyze complicated systems or problems, such as earthquakes, economic models or biological systems.

  • MAP 3305 - Engineering Mathematics 1

    Credits: 3

    Prerequisites: MAC 2312 - Analytic Geometry and Calculus 2  or MAC 2254 or MAC 2282
    Course Description:  

    The purpose of this module is to provide participants with the skills, knowledge and attitudes required to perform fundamental mathematical procedures and processes for solution of engineering problems, particularly the use of calculus, vector analysis and infinite series. The subject aims to show the relevance of mathematics to engineering and applied sciences.

  • MAP 3930 - Special Topics - Applied Mathematics

    Credits: 3

    Prerequisites: Consent of department head and instructor
    Course Description: This course investigates a topic of special interest to faculty and students that is outside regular course offerings.

  • MAP 4102 - Probability and Stochastic Processes

    Credits: 3

    Prerequisites: MAP 2302 - Differential Equations   (Amended 10/25/2021)
    Course Description: Probability Spaces, Discrete and Continuous Random Variables,  Conditional Probabilities, and Expectations, Standard Distributions, Poisson Processes, Discrete and continuous Parameter Markov Chains and either Queues, Brownian Motion or Simulation

  • MAP 4202 - Optimization Theory

    Credits: 3

    Prerequisites: MAP 4102 - Probability and Stochastic Processes  
    Course Description:  

    This course will focus on problem formulation, software technologies and analytical methods for optimization serving as an introduction to a wide variety of optimization problems and techniques including linear and nonlinear programming, dynamic programming, network flows, integer programming, heuristic approaches, Markov chains, game theory, and decision analysis.

  • MAP 4306 - Engineering Mathematics II

    Credits: 3

    Prerequisites: MAP 3305 - Engineering Mathematics 1  
    Course Description: The purpose of this module is to provide participants with the skills, knowledge and attitudes required to perform fundamental mathematical procedures and processes for solution of engineering problems, particularly the use of calculus, vector analysis and infinite series. The subject aims to show the relevance of mathematics to engineering and applied sciences.

  • MAP 4314 - Dynamical Systems

    Credits: 3

    Prerequisites: MAC 2313 - Analytic Geometry and Calculus 3  and MAP 2302 - Differential Equations  and MAS 3105 - Linear Algebra  
    Course Description: In this course, students will gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time. Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation.   

  • MAP 4341 - Applied Partial Differential Equations

    Credits: 3

    Prerequisites: MAP 2302 - Differential Equations  
    Course Description: This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

  • MAP 4413 - Fourier Analysis with Applications

    Credits: 3

    Course Description: The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Topics include: The Fourier transform as a tool for solving physical problems. Fourier series, the Fourier transform of continuous and discrete signals and its properties. The Dirac delta, distributions, and generalized transforms. Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems. The discrete Fourier transform and the FFT algorithm.

  • MAP 4484 - Mathematical Modeling in Biology I

    Credits: 3

    Prerequisites: MAP 2302 - Differential Equations  and MAS 3105 - Linear Algebra  
    Course Description: Introduction to techniques used in the construction, analysis, and evaluation of mathematical models. Modeling topics include: How fast will an infectious disease spread within a community? What fraction of a population need to be vaccinated in order to eradicate a disease, and what is the best vaccination policy? How stable is a given ecosystem? Students will learn how to frame a scientific question in mathematical terms; how to study the model using mathematical tools and techniques; how to interpret model predictions in the appropriate scientific context. 

  • MAP 4494 - Mathematical Modeling in Biology II

    Credits: 3

    Prerequisites: MAP 4484 - Mathematical Modeling in Biology I  
    Course Description: Introduction to techniques used in the construction, analysis, and evaluation of mathematical models. Modeling topics include: How fast will an infectious disease spread within a community? What fraction of a population need to be vaccinated in order to eradicate a disease, and what is the best vaccination policy? How stable is a given ecosystem? Students will learn how to frame a scientific question in mathematical terms; how to study the model using mathematical tools and techniques; how to interpret model predictions in the appropriate scientific context. 

  • MAP 5436 - Applied Math

    Credits: 3

    Prerequisites: None
    Course Description: This course covers probability, random processes, statistics, differential equations, special functions, Laplace and Fourier transforms for students with a level of mathematical maturity and experience comparable to that normally found in entering graduate students. The course will emphasize application of analytical methods to practical problems.

  • MAS 3114 - Computational Linear Algebra

    Credits: 3

    Prerequisites: MAC 2312 - Analytic Geometry and Calculus 2  with a grade of C or higher
    Course Description: Linear equations, matrices, and determinants; vector spaces and linear transformations; inner products and eigenvalues. This course emphasizes computational aspects of Linear Algebra.

  • MAT 4910 - Applied Mathematics Capstone 1 (Amended 10/25/2021)

    Credits: 3

    Course Description: This course is part one of the senior capstone sequence for the Engineering Mathematics degree. Students will conduct intensive research and produce significant written documentation of an experiment, research exploration, or special interest project in technology. This course meets communication/writing-intensive requirements (W).

  • MAT 4911 - Applied Mathematics Capstone 2 (Amended 10/25/2021)

    Credits: 3

    Prerequisites: MAT 4910 - Engineering Math Capstone 1  
    Course Description: This course is part two of the senior capstone sequence for the Engineering Mathematics degree. Students will conduct intensive research and produce significant written documentation of an experiment, research exploration, or special interest project in technology. This course meets communication/writing-intensive requirements (W).

  • MTG 4302 - Elements of Topology 1

    Credits: 3

    Prerequisites: MAS 3105 - Linear Algebra  
    Course Description: This course will present the basic concepts and examples of general topology. Topology provides a general setting for studying continuous mathematics, and is a foundation for much of pure and applied mathematics. Specific topics presented: basics of set theory and then introduce topological spaces and continuous functions, notions of connectedness, compactness, countability and separation, metric spaces and function spaces, and the notion of completeness.

  • MTG 4303 - Elements of Topology II

    Credits: 3

    Prerequisites: MTG 4302 - Elements of Topology 1  
    Course Description: This course will present the basic concepts and examples of general topology. Topology provides a general setting for studying continuous mathematics, and is a foundation for much of pure and applied mathematics. Specific topics presented: basics of set theory and then introduce topological spaces and continuous functions, notions of connectedness, compactness, countability and separation, metric spaces and function spaces, and the notion of completeness.

  • STA 2023 - Statistics 1

    Credits: 3

    Prerequisites: None
    Course Description: This course covers probability, random variables, hypothesis testing, confidence interval estimation, small sample methods, correlation, simple linear regression, and nonparametric statistics.

  • STA 3032 - Probability and Statistics

    Credits: 3

    Prerequisites: MAC 2312 - Analytic Geometry and Calculus 2  with a grade of C or higher
    Course Description: This course is a survey of the basic concepts in probability and statistics with applications in electrical, mechanical, and civil engineering. Topics include probability, common discrete and continuous probability distributions, estimation and hypothesis testing, and simple regression.

    **This course is not equivalent to STA 3036 - Probability and Statistics for Business, Data Science, and Economics and will not be approved as a substitution if you change majors into DSBA.

  • STA 3162C - Applied Statistics

    Credits: 3

    Prerequisites: STA 3441 or MAC 2311 - Analytic Geometry and Calculus 1  
    Course Description: Inferential statistics from an applied point of view. Probability and sampling distributions, confidence intervals and hypothesis testing, ANOVA, correlation, simple and multiple linear regressions.

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