Mathematics

**Stavros Christofi, Chair**

christofis@wcsu.edu

Higgins Hall 101N, Midtown Campus

(203) 837-9351

(203) 837-8289 (fax)

* David Burns, Associate Chair (Sabbatical Spring 2021)
*burnsd@wcsu.edu

Higgins Hall 101A, Midtown campus

(203) 837-9346

**Cathy Desisto-Reynolds, Department Secretary**

reynoldsc@wcsu.edu

Higgins Hall Office Suite 101 Reception, Midtown Campus

(203) 837-9299

(203) 837-8289 (fax)

**Faculty**

D. Burns, Assoc. Chair

S. Christofi, Chair

B. Hall

S. Hayes *(Sabbatical Fall 2020)*

S. Lightwood

A. Lubell

P. Maida

C. Rocca

M. Shoushani

T. Trimble *(Visiting Assistant Prof. Fall 2020)*

X. Wang

**Adjunct Faculty**

M. Aldrich | M. Alexandru | W. Barrett |

J. Breen | D. Ciskowski | J. DiGiacomo |

P. Ganchev | C Hall | R. Hopkins |

E. Lehman | W. Newsom-Stewart | H. Q. Nguyen |

P. O’Donnell | C. Peterson | K. Pisano |

M. Saccucci | K. Sherman | C. Wallace |

Overview

In the exciting, technologically advanced, and dynamic age we live in, mathematics has become one of the primary players in developing useful solutions to practical problems, receiving its rightful recognition as one of the foundational components of discovery and innovation.

Employers from businesses and government agencies to schools and foundations understand more and more the benefits of hiring an employee with quantitative competencies able to think abstractly, critically, and problem-solve — an employee with the skills that mathematics teaches.

Math Students at WCSU may choose major options in pure or applied mathematics or math education and are challenged to gain mastery in a variety of mathematical areas while fulfilling all requirements of a liberal arts education. The B.S. in Applied and Computational Mathematics as well as the B. S. in Secondary Education – Mathematics weave career applications into the curriculum. All programs are flexible and up-to-date.

Students have the opportunity to pursue their particular mathematical interests by working closely with Western’s dedicated mathematics professors on independent research projects. These may be in such diverse areas as analytical and numerical methods for partial differential equations, combinatorics, actuarial math, axiomatic set theory, cryptology, data science and machine learning, wavelets, topological measure theory, scientific computing, 3-D printing and more.

For students who plan to continue with graduate studies in mathematics, applied mathematics or a related field, as well as those who look forward to beginning a career upon graduation, studying mathematics at Western will provide the knowledge and skills required to achieve success.

Mission

It is the mission of the mathematics department to contribute to our society’s mathematical competency in a manner consistent with the university’s mission. To accomplish this, the department has defined its goals for the following three constituencies.

- The department supports the development of the mathematics student by providing students with:
- A breadth of knowledge in core areas of mathematics.
- A depth of knowledge in a specific area.
- Strong skills in mathematical communication, problem-solving, mathematical reasoning, and applications to related areas.
- Personalized learning experience in mathematics.

- The department supports the mission of the university by:
- Developing mathematical literacy for all students.
- Meeting the mathematical needs of all majors.
- Providing expertise in mathematics, applied mathematics, math education, and statistics.
- Conducting theoretical and applied research in the mathematical sciences.
- Maintaining a wide presence in the university community outside the department.

- The department supports the needs of the community by:
- Providing expertise in mathematics, math education, and statistics.
- Conducting research in the mathematical sciences.
- Providing continuing education and retraining in mathematics, applied mathematics, and mathematics-based fields.
- Fostering the appreciation of mathematical sciences.

**University Mathematics Testing and Placement Program**

All students admitted to the university are assigned mathematics placement prior to registration. Placement level is determined primarily by SAT scores. A placement test is available during the first class meeting for those students placed into developmental math in the Math Emporium, but wish to place higher. The purpose of the placement/testing is to determine whether the student possesses the basic quantitative skills needed for success in college-level quantitative studies.

If the student requires additional work in the skills area (SAT below 570), placement will be in MAT 098 Elementary Algebra, MAT 100P Intermediate Algebra Plus or MAT 100 Intermediate Mathematics. Otherwise, the student may opt for any general education course appropriate to the student’s educational goals. Students wishing to register for Calculus must have an SAT score of 620 or above. A 3, or higher, in AP Calculus AB allows a student to earn credit for Calculus I MAT 181. Detailed information regarding placement testing and placement levels can be found on the departmental website **(http://www.wcsu.edu/math/placement-testing/ )**.

**Instruction in MAT 098, MAT 100 and MAT 100P**

MAT 098, MAT 100 and 100P are taught following the Emporium Model of instruction. Traditional lecture methods are reduced and the emphasis is placed on individual work and one-on-one help from an instructor or teaching assistant. The text, homework assignments and course exam preparations are part of an online delivery system. Exams, including the final, are given as traditional paper and pencil tests. This should not be confused with an online class as daily attendance is required. Students use a required software program, ALEKS, Assessment and E-Learning in Knowledge Spaces, that guides them to the necessary videos, learning content and required practice assignments needed during the learning process. Meeting weekly assignment goals as well as the completion of the periodic progress checks and self assessments are mandatory and are incorporated into the student’s final grade. These courses are designed to have the student constantly engaged in the learning process using adaptive learning technologies. A professor and/or teaching assistants are always present during the lab’s open hours and available to teach/help/guide a student when needed, but there is little “Chalk and Talk” in the traditional sense.

** Thomas Grant, Math Emporium Coordinator**granttt@wcsu.edu

Higgins Hall 122A, Midtown Campus

(203) 837-9370

(203) 837-8289 (fax)

Degree Programs in Mathematical Sciences

**Bachelor of Arts**

Mathematics

Mathematics with Computer Science Option

**Bachelor of Science**

Applied and Computational Mathematics with options in:

- Mathematics of Data Science and Machine Learning
- Actuarial Science
- Applied Differential Equations and Scientific Computing

Secondary Education: Mathematics (in collaboration with the Education and Educational Psychology Department)

**Minor Programs**

Mathematics

**Bachelor of Arts in Mathematics (B.A.)**

Requirements:

__Part 1: General Education Competency Requirement__

See: ( http://wcsu.edu/catalogs/undergraduate/academic-programs-degrees/ )

All math majors must complete the university’s general education requirements. See description here:

__Part 2: General Education Exploration Requirements (40 cr.)__

You need to complete a total of 40 credits outside your major; this includes the required cognate courses listed below as well as any other courses outside your major.

WRT 101: Composition I (Writing Tier 1)

CS 140 Intro to Programming or CS 143 Visual Basic

Sequence Option: Choose from 1 of: BIO 103/104 or CHE 110/111 or PHY 110/11 or ECO 211/213

__Part 3:Major Requirements (45 cr.) __

Courses with ✢ require a C or better.

MAT 150 & 151: Math Seminar I & II

MAT 141: Foundations in Discrete Math ✢

MAT 182: Calculus II ✢

MAT 185: Math with Symbolic Computation

MAT 207: Proofs ✢

MAT 222: Introductory Statistics

MAT 272: Introduction to Linear Algebra ✢

MAT 281: Calculus III ✢

MAT 282: Differential Equations

MAT 332: Intro. to Applied Math ✢

MAT 375: Algebraic Structures ✢

MAT 383: Introduction to Analysis ✢

MAT 453 Senior Seminar Experience

MAT 467 Topics Sequence Elective

Choose 1 Department Approved Elective (MAT 250, 251, 298, 299, 342, 351, 359 or 363)

__Part 4: General Electives (35 cr.)__

MAT 181: Calculus I or MAT 170/171

Take additional credits to earn a total of at least 120 credits.

**Course Restrictions **

For a complete list of prerequisites, corequisites and other restrictions for all courses, please consult the Course Description section of this catalog.

Bachelor of Arts: Mathematics with Computer Science Option (B.A.)

__Part 1: General Education Competency Requirement__

See: ( http://wcsu.edu/catalogs/undergraduate/academic-programs-degrees/)

All math majors must complete the university’s general education requirements. See description here:

__Part 2: General Education Exploration Requirements (40 cr.)__

You need to complete a total of 40 credits outside your major; this includes the required cognate courses listed below as well as any other courses outside your major.

WRT 101: Composition I (Writing Tier 1)

Lab Science Sequence Option: Choose from 1 of: BIO 103/104 or CHE 110/111 or PHY 110/11 or PHY 120/121

__Part 3:Major Requirements (45 cr.) __

Requirements:

Courses with ✢ require a C or better.

MAT 150 & 151: Math Seminar I & II

MAT 182: Calculus II ✢

MAT 207: Proofs ✢

MAT 272: Introduction to Linear Algebra ✢

MAT 281: Calculus III ✢

MAT 375: Algebraic Structures ✢

MAT 453: Senior Seminar Experience

MAT 165: Introductory Discrete Math ✢

Choose 1 of: MAT 222 Introductory Statistics or MAT 282 Differential Equations

Choose 1 of: MAT 332 Intro. to Applied Math or MAT 359 Theory of Computation

CS 170: Computer Science I: Language

CS 205: Data Modeling and Database Design

CS 315: Design and Analysis of Algorithms

Choose 1 CS Engineering Elective: CS 305 or CS 350 or CS 360

__Part 4: General Electives (35 cr.)__

MAT 181: Calculus I or MAT 170/171

Choose 1 of: CS 140: Introduction to Programming or CS 143 Visual Basic

Take additional credits to earn a total of at least 120 credits

Learning Outcomes

At the completion of their B.A. in Mathematics:

- Students will communicate mathematics in written form, using appropriate mathematical writing conventions.
- Students will read, explain and create mathematical exposition.
- Students will analyze, model and solve problems.
- Students will be required to demonstrate proficiency in a variety of technological tools (computer algebra systems, visualization software, statistical packages and some computer programming language).

*For those completing a BS in Secondary Education,* students will demonstrate competence in the 16 standards for preparation of mathematics teachers as set by the National Council of Teachers of Mathematics. These standards are:

- Knowledge of Mathematical Problem Solving
- Knowledge of Reasoning and Proof
- Knowledge of Mathematical Communication
- Knowledge of Mathematical Connections
- Knowledge of Mathematical Representation
- Knowledge of Technology
- Dispositions
- Knowledge of Mathematics Pedagogy
- Knowledge of Number and Operation
- Knowledge of Different Perspectives on Algebra
- Knowledge of Geometries
- Knowledge of Calculus
- Knowledge of Discrete Mathematics
- Knowledge of Data Analysis, Statistics, and Probability
- Knowledge of Measurement
- Field-Based Experiences

More information about specific indicators can be found on the Math department website at www.wcsu.edu/math.

**Bachelor of Science in Applied and Computational Mathematics (B.S.)**

**Requirements:**

In addition to the courses listed below, students must complete all university general education requirements and sufficient additional free electives to total a minimum of 120 semester hours, including foreign language and physical education.

*All Option Areas Must Take:*

MAT 141 – Foundational Discrete Math

MAT 150 – Math Seminar I

MAT 151 – Math Seminar II

MAT 181 – Calculus I

MAT 182 – Calculus II

MAT 207 – Proofs

MAT 222 – Introductory Statistics

MAT 272 – Linear Algebra

MAT 281 – Calculus III

MAT 282 – Ordinary Differential Equations

MAT 322 – Probability

MAT 332 – Applied Linear Algebra and Math of Machine Learning

MAT 380 – Math Modeling with Symbolic and Scientific Computations

MAT 383 – Introduction to Mathematical Analysis

MAT 453 – Senior Seminar (CE,W3) (OR SIS with Project) (OR Senior Thesis) (OR Internship)

**Further Requirements (Option Specific)**

**Mathematics of Data Science and Machine Learning Option:**

Further Required MAT Courses

MAT 422 – Statistics for Data/Actuarial Science and Machine Learning

MAT 470 – Applications of Machine Learning and Wavelets

*One of the following:
*MAT 468 – Partial Differential Equations

MAT 469 – Numerical Methods for Ordinary and Partial Differential Equations (OPDEs)

Cognates

PHI 227 – Ethics in Computing

CS 140 – Introduction to Programming (Python)

Application Area Courses:

CS 172 – Intermediate Java Programming

CS 205 – Data Modeling and Database Design

CS 250 – Introduction to Data Structures, Algorithms and Complexity

CS 303 – Introduction to Data Science with Python

**Applied Differential Equations and Scientific Computing Option:**

Further Required MAT Courses

*Regardless of the sequence pursued, students interested in this option must take:*

MAT 468 – Partial Differential Equations

MAT 469 – Numerical Methods for Ordinary and Partial Differential Equations (OPDEs)

MAT 470 – Applications of Machine Learning and Wavelets

Cognates

Cognates (Sequence CHE)

CS 140 – Introduction to Programming (Python)

Cognates (Sequence MTR)

CS 140 – Introduction to Programming (Python)

PHY 110 – General Physics I (Calculus)

Application Area Courses

Currently, students interested in this option will need to pick one of the following sequences to pursue: a chemistry sequence (CHE) or meteorology sequence (MTR). For students interested in other application areas, please contact the department chair.

Sequence CHE

CHE 110 – General Chemistry I

CHE 111 – General Chemistry II

CHE 300 – Physical Chemistry I

CHE 301 – Physical Chemistry II

Sequence MTR

PHY 111 – General Physics II (Calculus)

MTR 310 – Atmospheric Thermodynamics

MTR 311 – Atmospheric Dynamics

MTR 340 – Mesoscale Meteorology and Numerical Forecasting

**Actuarial Science Option:**

Further Required MAT Courses

MAT 329 – Actuarial Mathematics

MAT 422 – Statistics for Data/Actuarial Science and Machine Learning

*One of the following:*

MAT 468 – Partial Differential Equations

MAT 469 – Numerical Methods for Ordinary and Partial Differential Equations (OPDEs)

MAT 470 – Applications of Machine Learning and Wavelets

Cognates

CS 143 – Visual BASIC

Application Area Courses

ACC 201 – Financial Accounting

ECO 211 – Principles of Macroeconomics

ECO 213 – Principles of Microeconomics

FIN 310 – Principles of Finance

**Learning Outcomes:**

The BS in Applied and Computational Math program will graduate students who will:

- Demonstrate possession of a resilient mathematical foundation that allows them to reason rigorously in mathematical arguments and that is adaptable to current and future trends. This foundation encompasses the core areas of:
- Real and numerical analysis

b. Differential equations

c. Linear algebra

d. Probability and statistics - Connect different areas of mathematics with other disciplines and demonstrate proficiency in at least one of the following modern applications:
- Data Science and Machine Learning

b. Scientific Computing (coupled with a specific discipline/application area)

c. Actuarial Science. - Demonstrate an ability to synthesize and apply major theoretical and/or computational techniques and concepts to analyze, construct, and solve realistic models of practical importance and:
- Recognize the limitations of the theoretical concepts in building solutions to real-world problems
- Adapt theoretical ideas to develop efficient numerical solutions to real-world problems
- Adapt theoretical ideas to develop efficient algorithms that can be applied to real-world problems.
- Use relevant software and technology (such as MATLAB, Mathematica, Python, and LaTeX) and/or write computer programs to construct, visualize, analyze, and interpret solutions to applied mathematical problems.
- Be able to, working independently or collaboratively, apply concepts learned either from relevant coursework, possible internships, or research projects with faculty, to write mathematical reports that effectively communicate findings to others (for instance, other classmates and/or attendees at local/international conferences or research symposia such as Western Research Day), and that can serve as the basis for possible publications.

**Bachelor of Science in Secondary Education – Mathematics (B.S.)**

__Part 1: General Education Competency Requirement__

See http://wcsu.edu/catalogs/undergraduate/academic-programs-degrees/__ __

__Part 2: General Education Exploration Requirements (40 cr.)__

You need to complete a total of 40 credits outside your major; this includes the required cognate courses listed below as well as any other courses outside your major.

WRT 101: Composition I

CS 140 Intro to Programming

Fine Arts class

Lab Science class (that satisfies Scientific Inquiry)

HIS 148 or 149

__Part 3:Major Requirements (80 cr.) __

__Math Requirements (43 cr.)__

MAT 150 & 151: Math Seminar I & II

MAT 141: Foundations in Discrete Math

MAT 181: Calculus I or MAT 170/171

MAT 182: Calculus II

MAT 207: Proofs

MAT 212: Math in the Middle Grades

MAT 222: Introductory Statistics

MAT 242: Foundations of Geometry

MAT 272: Introduction to Linear Algebra

MAT 281: Calculus III

MAT 342: Topics in Geometry

MAT 375: Algebraic Structures

Choose one of: MAT 363 History of Math or MAT 383 Intro. to Analysis

Choose one other 200-400 level math course

__Certification Requirements (37 cr.)__

You must earn a B or better in each of the following.

ED 206: Introduction to Education

ED 212: Educational Psychology II

HPX 215: Health Issues in Schools

ED 385: Methods of Teaching

ED 386: Secondary Education Professional Dev.

ED 405: Introduction to Special Education

ED 440: Integrating Language

ED 449: Teaching Math in Secondary Schools

ED 340: Assessment of Teaching Strategies

ED 342: Student Teaching (Pass/Fail)

See the Department of Education and Educational Psychology within the School of Professional Studies.

The following are suggested course selections for mathematics majors. Due to the diversity of students’ backgrounds, students must consult with their (math faculty) adviser to select the program sequence that best fits their needs. For example, students with an inadequate math background may have to begin with MAT 170 instead of MAT 181. B.S. majors (secondary education) have a professional semester in the fall and student teaching in the spring of their senior year.

Mathematics (B.A.)

**Freshman Year**

Fall Semester |
Spring Semester |

MAT 150 | MAT 151 |

MAT 181 | MAT 182 |

MAT 141 |

**Sophomore Year**

Fall Semester |
Spring Semester |

MAT 185 | MAT 222 |

MAT 207 | MAT 272 |

MAT 281 | MAT 282 |

MAT 375 |

**Junior Year**

Fall Semester |
Spring Semester |

MAT 332 | MAT 467 |

Science Sequence I | Science Sequence II |

MAT 383 |

**Senior Year**

Fall Semester |
Spring Semester |

Math elective | MAT 453 |

Math elective |

** **

Mathematics – Secondary Education (B.S.)

**Freshman Year**

Fall Semester |
Spring Semester |

MAT 150 | MAT 151 |

MAT 181 | MAT 182 |

MAT 141 |

**Sophomore Year**

Fall Semester |
Spring Semester |

MAT 207 | MAT 222 |

MAT 281 | MAT 272 |

MAT 212 |

**Junior Year**

Fall Semester |
Spring Semester |

MAT 242 | MAT 342 |

MAT 375 | |

Math elective |

**Senior Year**

Fall Semester |
Spring Semester |

Professional semester | Student teaching |

Minor in Mathematics

At least 17 credits in major mathematics courses, including MAT 171 or 181, and MAT 182. In addition, the student must achieve a GPA of 2.0 or better in the courses used to fulfill the minor requirements.