# Mathematics

As part of the College of Arts and Sciences, the Department of Mathematics and Computer Sciences prepares students for careers as engineers, actuaries, scientists, educators, and technicians, while concurrently striving to inspire our students to love the subject itself. We offer majors in: Mathematics and Computer Science.

The study of Mathematics is a balancing act between application and theory. Mathematicians enjoy pattern seeking, conjecture making, and articulate arguments, and we want our graduates to go into the world motivated by curiosity and armed with the skills that are hallmarks of mathematicians.

Our curriculum is structured to encourage students to take a variety of courses. During their first two years, students complete 12 credits of Calculus, along with courses in Linear Algebra, Differential Equations, and Set Theory and Logic. After the students have a strong foundation in the fundamentals of Mathematical Theory, they have the option to take course from topics ranging from Abstract Algebra, Real and Complex Analysis (appropriate for students interested in Graduate School) to Statistics and Actuarial Sciences (appropriate for students interested in a career in industry). With the availability of directed readings and independent studies, students have the ability to customize their mathematical studies to suit their personal interests.

For information about the Mathematics Minor, click here.

*“I would not be where I am today without Misericordia and our wonderful math department. Our professors gave me the confidence I needed as an incoming freshman that has strengthened my performance in the classroom and overall experience. I immediately participated in the Math and Computer Science Club and became the president in my sophomore year. With the help of our professors, the club, and our guaranteed placement program (GPP), I am excited to pursue a career in mathematics and statistics and work towards creating advanced statistics programs in our local schools."*

~ Lindsay Kane

Junior, Class of 2020

Mathematics, Statistics, and Sec. Ed. Major

President of the Math and Computer Science Club

#### Fast Facts and Outcomes

The study of Mathematics is a balancing act between **application **and **theory**. Our curriculum is designed to provide a **diverse **and **solid background **in various areas of Mathematics. Current faculty **research interests **are wide-ranging and include Approximation Theory, Statistics, Topology, Logic, Chaos Theory, Computational Biology, Scientific Computing, Graph Theory, and the History of Mathematics; we also have a faculty specialist in Actuarial Science.

**What makes Misericordia’s Mathematics program stand out from all the rest: **

Our students will study cutting-edge modern Mathematics while also learning classical mathematical results and techniques and their history. By way of Mathematics electives, our major program can be tailored to lead you to a wide variety of career choices such as Actuarial Science, Secondary Education, Statistics, Applied Mathematics, or to prepare you for further studies in graduate school mathematics.

**Mathematics Minor: **Students from other majors can complete a minor in Mathematics by taking 6 MTH courses as described in the catalog.

**Double Major: **The Mathematics major combines well with others majors like Statistics or Computer Science.

**Program degree options: **

- Mathematics Bachelor of Arts
- Mathematics Bachelor of Arts, (Pre-DPT Specialization)
- Mathematics Bachelor of Arts, (Secondary Education Certification)
- Mathematics Bachelor of Science

**Job opportunities for a Mathematics degree include the following fields: **

- Teaching
- Cryptographer
- Mathematician
- Actuary
- Financial Planner
- Statistician
- Investment Analyst/Control
- Government
- Systems Engineer
- Budget Analyst
- Operations Research
- Accountant
- Purchase Agent
- Insurance Underwriter
- Market Researcher
- Cost Estimator
- Software Tester

**Research/internships and other opportunities available via: **

- Summer Undergraduate Research Fellowships (SURF)
**Internships**are available with many local businesses and organizations including the Wilkes-Barre/Scranton Railriders; Berkshire Hathaway Guard Insurance Co.; and Masonic Villages**Student Clubs/Activities:**Math and Computer Science Club

**Mathematics alumna have gone on to achieve employment at: **

- Telcordia Technologies
- AT&T
- Schott Glass of North America
- General Electric
- Alltel Information Services, Inc.
- New York Life Investment Management
- Juniper Networks
- Metropolitan Life
- IBM Corporation
- Procter & Gamble, Inc.
- Prudential Insurance Corp.
- Numerous School Districts across the U.S.
- Honeywell Hometown Solutions

**Misericordia Mathematics majors have also continued on to graduate programs at: **

- Binghamton University (Mathematics)
- Boston University (Bio Statistics)

#### Mathematics Major

The department offers both a Bachelor of Arts and a Bachelor of Science in Mathematics.

The required mathematics courses for either degree are the same. Students who choose a Bachelor of Arts must complete two semesters of physics; those choosing a Bachelor of Science must complete two semesters of physics and either two semesters of chemistry or of biology.

Here is the description of the **mathematics major** from the 2017 catalog.

Here is a **year-by-year breakdown** of what we suggest that a mathematics major takes.

The mathematics department pays the membership fees for our majors and minors to the Mathematical Association of America.

**SECONDARY EDUCATION**

We also offer a Bachelor of Arts with a Secondary Education certification. The secondary education program is designed to prepare teachers of mathematics for grades 7 to 12. Our program is continually refined to keep pace with developments in the profession; for example, the program prepares teachers to effectively deal with students with disabilities. It is approved by the Pennsylvania Department of Education and leads to a PA Instructional certificate. The University's recommendation and the successful completion of other requirements established by the state, including meeting the pass scores specified by PDE on the required battery of certification tests, qualify graduates for a PA Instructional I Certificate.

Here is the description of the mathematics major's **secondary education** program from the 2017 catalog.

**DOUBLE MAJOR WITH MATHEMATICS**

Thanks to the high number of electives within the mathematics major, many students double major in another field, most commonly a science, but also disciplines within the humanities. We are glad that so many students opt to double major, as we believe that this contributes to a well-rounded education that not only prepares students for a variety of careers, but also shapes students into articulate and hospitable citizens.

#### Course Sequence

First Year | |||

First Semester | Credits | Second Semester | Credits |

CPS 101 Intro. to Programming | 3 | MTH 172 Calculus II | 4 |

MTH 171 Calculus I | 4 | MTH 244 Set Theory & Logic | 3 |

Core | 3 | Core | 3 |

Core | 3 | Core | 3 |

Core | 3 | Core | 3 |

Total Credits | 16 | Total Credits | 16 |

Sophomore Year | |||

First Semester | Credits | Second Semester | Credits |

MTH 226 Calculus III | 4 | MTH 215 Mathematical Statistics | 3 |

MTH 241 Linear Algebra | 3 | MTH 242 Differential Equations | 3 |

PHY 221 General Physics I | 4 | PHY 222 General Physics II | 4 |

Core | 3 | Core | 3 |

Core | 3 | Core | 3 |

Total Credits | 17 | Total Credits | 16 |

Junior Year | |||

First Semester | Credits | Second Semester | Credits |

MTH 463 Abstract Algebra I | 3 | Mathematics elective | 3 |

Mathematics elective | 3 | Mathematics elective | 3 |

Mathematics elective | 3 | Core | 3 |

Core | 3 | Core | 3 |

Free elective | 3 | Free elective | 3 |

Total Credits | 15 | Total Credits | 15 |

Senior Year | |||

First Semester | Credits | Second Semester | Credits |

MTH 441 Real Analysis I | 3 | Free elective | 3 |

Mathematics elective | 3 | Free elective | 3 |

Core | 3 | Free elective | 3 |

Core | 3 | Free elective | 3 |

Free elective | 3 | ||

Total Credits | 15 | Total Credits | 12 |

Total required for graduation: 122 credits |

#### Course Descriptions

In addition to our regularly scheduled courses, the department offers independent studies and special topics courses. Some recent examples include:

- Vector Calculus
- φ, π, e and i
- Calculus 4: Stokes Theorem and Differential Forms
- Graph Theory

**MTH 108 Precalculus, 3 credits**

Linear equations, inequalities, functions, graphing, logarithms and exponentials, circular functions. (added 9/10/2014; course to be offered Spring 2014)

**MTH 115 Basic Statistics, 3 credits**

An introduction to the use of statistical methods with emphasis on practical applications. Descriptive statistics, introduction to probability, estimation of parameters, introduction to hypothesis testing, correlation, and linear regression.

**MTH 116 Basic Statistics II, 3 credits**

Hypothesis testing, analysis of variance, correlation and regression analysis, nonparametric statistics. *Prerequisite: MTH 115*

**MTH 120 Mathematical Reasoning, 3 credits**

Development of quantitative problem solving. Methods of problem solving. Reading, determining, and solving problems using basic arithmetic, algebra, and geometry. Common mathematical models of everyday phenomena.

**MTH 160 Discrete Mathematics, 3 credits**

Emphasizes the application of discrete mathematics, including combinatorics, graphs, recursively defined sequences, social choice, fair division, etc.

**MTH 165 Survey of Calculus, 3 credits**

A one-semester survey of the fundamental principles of calculus; topics include functions, limits, derivatives, definite integrals and applications. May not be taken by students who have previously received credit for MTH 151 or MTH 171.

*Fall and Spring*

**MTH 171 Calculus I, 4 credits**

Functions, limits, continuity, derivatives, definite integrals, and applications.

*Fall*

**MTH 172 Calculus II, 4 credits**

Transcendental functions, techniques of integration, sequences, series, and applications.

*Prerequisite: MTH 171: Calculus I*

*Spring*

**MTH 200 History of Mathematics, 3 credits**

The place of mathematics in human enterprise and the central role it has played in the development of civilization. Topics chosen include the history of mathematics, contributions by various cultures, geometry, calculus, number theory, modern logic, and unsolved problems.

*Prerequisite: MTH 165 or MTH 171. Fall (odd years only)*

**MTH 210 Discrete Structures, 3 credits**

Provide students with the definitions and basic tools for reasoning about discrete mathematical objects useful for computer science.

*Prerequisite: MTH 171 or equivalent.*

**MTH 215 Mathematical Statistics, 3 credits**

Probability theory, games of chance, probability distributions, testing of hypotheses, curve fitting, and correlation.

*Prerequisite: MTH 172. Spring (odd years only)*

**MTH 226 Calculus III, 4 credits**

Vectors, multivariable and vector-valued functions, partial derivatives, multiple integrals, and applications.

*Prerequisite: MTH 172 Fall*

**MTH 241 Linear Algebra, 3 credits**

Systems of linear equations, vector space, inner products, determinants, eigenvalues and eigenvectors, and applications.

*Prerequisite: MTH 172 or permission of the instructor.*

*Fall (odd years only)*

**MTH 242 Differential Equations, 3 credits**

Equations of first order and degree, higher order, and degree equations, including linear with constant coefficients, and systems of equations.

*Prerequisite: MTH 172 or its equivalent. Spring*

**MTH 244 Set Theory and Logic, 3 credits**

Introduction to set theory, equivalence and order, Boolean algebra, introduction to logic, and rules of inference.

*Prerequisite: MTH 171 or permission of the instructor. Spring*

**MTH 315 Mathematical Statistics II, 3 credits**

Multivariate distributions. Estimation and hypothesis tests for multiple parameters. Regression and correlation. Analysis of variance.

*Prerequisites: MTH 215 and MTH 226.*

**MTH 320 Actuarial Mathematics I, 3 credits**

Applying probability theory to problems in actuarial science, finance and insurance; utilizing discrete, continuous and multivariate distributions.

*Prerequisites: MTH 215 and MTH 226.*

**MTH 351 Geometry, 3 credits**

History of geometry, axiom systems, types of geometries, and axiomatic development of a geometric theory.

*Fall (even years only)*

**MTH 390 Methods of Teaching Math, 3 credits**

This course is designed to introduce candidates to the content needed to teach fourth through eighth grade math curricula and to the strategies used to develop math competencies at the middle level.

** **

**MTH 413 Math Cooperative Education, 3-6 credits**

Academic study combined with work experience in the community.

**MTH 420 Actuarial Mathematics II, 3 credits**

Solving problems in finance. Variation of annuities, loan repayment, bond valuation and the term structure of interest rates. Measuring rates of return.

*Prerequisite: MTH 320*

**MTH 422 Linear Algebra II, 3 credits**

Real and complex vector spaces, bases and dimension, linear operators, eigenvalues and eigenvectors, spectral theorems.

*Prerequisite: MTH 241 or its equivalent.*

**MTH 423 Complex Variables, 3 credits**

Analytic and elementary functions, differentiation, Cauchy's Theorem, power series, calculus of residues.

*Prerequisite: MTH 226 or its equivalent.*

*Spring (even years)*

**MTH 425 Topology, 3 credits**

Topological spaces, mappings and homeomorphisms, connected spaces, compact spaces.

*Prerequisite: MTH 244 Spring (odd years)*

** **

**MTH 441 Real Analysis I, 3 credits**

(Formerly MTH 341) Real number system, topology, sequences, limits, continuity, and differentiability.

*Prerequisites: MTH 226, MTH 244. Spring (even years only)*

**MTH 442 Real Analysis II, 3 credits**

(Formerly MTH 342) Continuation of MTH 441, including measure and integration.

*Prerequisite: MTH 441. Fall (even years only)*

**MTH 463 Abstract Algebra I, 3 credits**

(Formerly MTH 363) Introduction to abstract algebra, groups, and introduction to rings and fields.

*Prerequisite: MTH 244. Spring (odd years only)*

** **

**MTH 464 Abstract Algebra II, 3 credits**

(Formerly MTH 364) Rings, integral domains, fields, and polynomials.

*Prerequisite: MTH 463. Fall (odd years only)*

**MTH 480 Independent Study, 1-3 credits**

Special investigation of a selected topic.

*(On demand)*

**MTH 486 Special Topics in Mathematics, 1-3 credits**

Topics vary from semester to semester and will be announced with preregistration information.

**MTH 490 Mathematics Seminar, 3 credits**

Prerequisite: Permission of department.

*(On demand)*

#### Math Club

The Math Club gives students an opportunity to discuss and investigate mathematics outside of the classroom.

The current leadership of the club:

- Tara Koskulitz - President
- Lindsay Kane - Secretary
- Michael Gottstein - Treasurer

Recent and ongoing research projects include:

- Tara Koskulitz and Mike Gottstein were awarded a Summer 2016 stipend research on the game KAMI and its relationship to graph theory
- Taylor Rupp, Mike Gottstein, and Craig Siekierka are some of the previous Summer stipend recipients.

Other projects include:

- Fundraising for the club and for local charities
- A series of tutorial videos (posted to youtube) designed to help lower level mathematics students at the university
- A meal paid for and delivered by the club to a needy family at Thanksgiving

From the *Mountain Top Eagle -*

Misericordia University Teacher Education and Math Club students offered lessons on sorting, patterns, symmetry and fractions during a fun and entertaining Math Day at St. Jude School in Mountain Top. More than 30 Misericordia students provided fun and engaging ways for 200 students in pre-k through 8th grades at St. Jude to learn about and appreciate mathematics.

Steven Tedford, Ph. D., of Mountaintop, associate professor of mathematics at Misericordia University, and his wife, Veronica, a former collegiate professor of mathematics, coordinated the program.

The program culminated with St. Jude School students and Principal Sister Ellen Fischer, S. C. C., presenting a $250 check to Christine Somers, D. Min., director of Campus Ministry at Misericordia University.

Math Day is a service project for the Math Club and the service-learning component of the Intro to ECE and Math Methods II courses the teacher education majors are taking at Misericordia University. It is also an opportunity for the future teachers to gain hands-on experience working with children in a real-world learning environment and engaging them in activities that make math fun.

#### Mathematics Symposium

The Department of Mathematics at Misericordia University will be hosting the 9^{th} annual Luzerne and Lackawanna Counties Mathematics Symposium on Saturday, October 6, 2018.

**The symposium begins at 8:15 am with a continental breakfast. Talks begin at 9:00 am and continue until 2:00 pm.**

** **

**List of Speakers and Talks:**

1. Dr. Tania Hazra (Misericordia University)

**Title:** A super-Gaussian Poisson-Boltzmann model for electrostatic solvation energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states

**Abstract:** Calculations of electrostatic potential and solvation energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the calculation becomes challenging for the dielectric property across the solute-solvent boundary and interior cavities. To overcome these experimental challenges, a novel super-Gaussian dielectric PB model is presented in this work. Mathematically, an effective dielectric constant (EDC) analysis is introduced in this effort to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both cavity-fluids and empty cavities are employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in a biomolecular electrostatic analysis.

2. Dr. Jennifer Vasquez (University of Scranton)

**Title:** Entanglement: Topological and Quantum

**Abstract:** We will begin by discussing topological notions of entanglement such as braids and linking of knots. This will be followed by a discussion of quantum entanglement. Finally, time permitting, we will describe possible connections of different types of entanglement.

3. Dr. Soumyadip (Dip) Acharyya (Embry-Riddle Aeronautical University)

**Title:** To be Announced

**Abstract: **To be Announced

4.** **Lindsay Kane (Misericordia University)

**Title: **An Introduction to Fibonacci Graphs

**Abstract:** The Fibonacci numbers have been studied for centuries by many people using a large variety of techniques. When considered combinatorially, these numbers can be translated into graphs. We introduce these graphs and discuss some of the basic properties of them, which arise from this combinatorial interpretation of the Fibonacci numbers.

5. Dr. Steven Tedford (Misericordia University)

**Title: **Fibonacci Graphs continued.

**Abstract: **We will continue the introduction to Fibonacci graphs given by Lindsay. In particular, we will look at some structural results for these graphs as well as an infinite graph that represents the entire Fibonacci Sequence. Finally, we will consider similar graphic structures for additional combinatorial number sequences.

6. Dr. Michael Floren (Misericordia University)

**Title: ***What works best? The practical effects of model misspecification in determining statistical significance.*

**Abstact: **This talk will discuss a medical research example where model specification played a key role in determining (or not determining) treatment differences.

7. Dr. Karen McCready (King’s College)

**Title: **Properties of edge-colored 2-connected graphs

**Abstract: **An edge-colored path is properly colored if adjacent edges receive distinct colors. An edge- colored graph is properly connected if each pair of vertices in the graph is connected by at least one properly colored path. In such a graph we extend the idea of diameter to that of proper diameter, a function of both the graph and its coloring, which is defi to be the maximum length of a shortest properly colored path between any two vertices in the graph. We will explore the relationship between the diameter and proper diameter of certain graph classes and consider how proper diameter values relate to the vertex connectivity of a graph.

For more information, please contact Dr. StevenTedford at 570-674-6771 or stedford@misericordia.edu

#### Careers in Mathematics

The Mathematical Association of America provides a **Careers page** with links to research, data, articles, and books about what the nation's mathematics students can and do choose as careers.

#### Department News

The Mathematics Department at MU extends a hearty congratulations to our 7 Mathematics majors who graduated in May 2018. Shown in the photo above are 3 of our May graduates who are headed to graduate school in fall 2018. They are (l to r) Pat McGinty (Binghamton University, Mathematics), Tara Koskulitz (Binghamton University, Mathematics), and Blake Smith (Boston University, Biostatistics).

**Austin Galiardo** passed the Society of Actuaries Exam P (Probability) in Spring 2016 and Exam FM (Financial Mathematics) in Summer 2016

**Miles Westrich** (class of 2016) also passed the Society of Actuaries Exam P (Probability) in Summer 2016

**Michael Gottstein** and **Tara Koskulitz**, (students) presented "A Mathematical Approach to the Game of Kami" at the EPADEL Section of the Mathematical Association of America's Annual Spring Meeting at Kutztown University in April 2017.

**Dr. Yuhan Ding** presented her research paper titled “A Guaranteed Locally Adaptive Algorithm for Univariate Function Approximation and its Computational Cost” at the 2018 SIAM Annual Meeting in Portland, Oregon, in July 2018.

The Department of Mathematics at Misericordia University welcomes two new full-time faculty members. **Dr. Tania Hazra **and** Dr. Michael Floren** will be joining our department in the fall 2018 semester. Dr. Hazra’s research interests are in Scientific and Statistical Computing, and Computational Biology. Dr. Floren’s research interests are in (Applied) Statistics and Statistics Education.

#### Admissions Requirements

- Class rank in the top half of the high school graduating class and/or a cumulative 2.5 grade point average
- Minimum combined SAT score of 850 for Critical Reading and Math (combined) if taken prior to March 5, 2016, or 930 if taken after March 5, 2016. In lieu of the SAT, ACT results may be presented with a minimum required composite score of 18

#### Meet the Faculty

#### Testimonials

*“I would not be where I am today without Misericordia and our wonderful math department. Our professors gave me the confidence I needed as an incoming freshman that has strengthened my performance in the classroom and overall experience. I immediately participated in the Math and Computer Science Club and became the president in my sophomore year. With the help of our professors, the club, and our guaranteed placement program (GPP), I am excited to pursue a career in mathematics and statistics and work towards creating advanced statistics programs in our local schools."*

~ Lindsay Kane

Class of 2020

Mathematics, Statistics, and Sec. Ed. Major

President of the Math and Computer Science Club

*"I really enjoyed my experience as a Mathematics major at Misericordia University! In addition to my coursework, I had the opportunity to learn even more by doing research my last two summers. This research experience was extremely valuable because it helped me to realize that I would like to make doing research part of my future career.*

*I will be starting a doctorate program in mathematics at Binghamton University this fall, and I attribute a significant portion of my preparedness to my hard-working, caring professors at Misericordia University, as well as to the welcoming environment created by the faculty, staff, and students."*

~ Tara Koskulitz ‘18

B.A. Mathematics

*"I love being a math major at Misericordia. The faculty here really cares about your well being, the club is very involved on campus, and my fellow students are like family. We help each other out here, we thrive off each other. If we have questions we know that our teachers will be there to lend a helping hand. We’ve created a community here in the math department and I am so fortunate to be exposed to it. The math department has given me wonderful opportunities from hands on to personal experiences that will further advance me in my math career."*

Class of 2019

Mathematics Major