# Mathematics and Statistics

The Department of Mathematics and Statistics at Loyola University Chicago, in the College of Arts and Sciences, supports the Jesuit ideal of knowledge in the service of humanity. The department endeavors to advance knowledge in mathematics and statistics, engaged with Chicago, the nation and the world. To achieve this mission, the department participates in the discovery, development, demonstration and dissemination of professional knowledge and practice within a context of professional ethics and service to others.

Beyond honing students' analytical skills, the mathematics and statistics curricula also foster critical thinking and the ability to articulate it... skills that are in high demand in many diverse fields.

The Department of Mathematics and Statistics will work to ensure that we invest in each student’s success, sense of belonging, and cultural competency. We will strive to engage, empower, inform, and hold our faculty and students accountable for fostering an environment where every person shares in the responsibility for advancing diversity and inclusive excellence. Likewise, the department decisions and policies will be crafted with these goals in mind. We commit to this mission recognizing a definition of diversity that includes, but is not limited to, race, ethnicity, color, religion, national or ethnic origin, sex, age, military/veteran status, disability, marital status, sexual orientation, gender identity and expression, socio-economic background, and residency.

## Mathematics (MATH)

**MATH 401**

**Introduction to Graduate Study in Mathematics**

**(1 Credit Hour)**

*Pre-requisites:*Graduate Student status

**Outcomes**

Students will: gain practice reading, writing, listening to, and summarizing advanced mathematics; learn the pedagogical, ethical, and DEI matters associated with careers in the mathematical sciences; gain practice giving lectures, writing problem-sets, and grading mathematics; explore possible career trajectories**MATH 404**

**Probability & Statistics I**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH404/STAT404

**MATH 405**

**Probability & Statistics II**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH405/STAT405

**MATH 406**

**Stochastic Processes**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH406/STAT406

**MATH 409**

**Advanced Numerical Analysis**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP409/MATH409

**MATH 413**

**Algebra I**

**(3 Credit Hours)**

**MATH 414**

**Algebra II**

**(3 Credit Hours)**

**MATH 415**

**Topics in Linear Algebra**

**(3 Credit Hours)**

**MATH 416**

**Survey of Algebra**

**(3 Credit Hours)**

*Pre-requisites:*Graduate Student status

**Outcomes**

Students will demonstrate facility with standard proof techniques in abstract algebra, and the ability to work with algebraic structures (including actions, morphisms, and quotients; concretely and abstractly); Students will recognize the common theme of classification uniting the course topics**MATH 418**

**Combinatorial Mathematics**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP418/MATH418

**MATH 420**

**Topics in Mathematical Logic**

**(3 Credit Hours)**

**Outcomes**

Students will develop proof writing skills, expand mathematical literacy, understand the expressive power and limitations of propositional and predicate logics and learn the mathematical meaning of "truth" and "proof"**MATH 422**

**Advanced Topics in Number Theory**

**(3 Credit Hours)**

*Pre-requisites:*MATH 201 or the equivalent or permission of the instructor

**Outcomes**

Understand the importance of historically significant concepts and problems in number theory; Understand the proofs of related theorems; Solve problems and prove theorems from topics covered in class**MATH 428**

**Algebraic Coding Theory**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP428/MATH428

**MATH 431**

**Cryptography**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP431/MATH431

**MATH 443**

**Intro to Algebraic Topology**

**(3 Credit Hours)**

**MATH 444**

**Topics in Geometry**

**(1-3 Credit Hours)**

**MATH 445**

**Financial Math Derivatives**

**(3 Credit Hours)**

**MATH 451**

**Analysis I**

**(3 Credit Hours)**

**MATH 452**

**Analysis II**

**(3 Credit Hours)**

**MATH 453**

**Complex Analysis**

**(3 Credit Hours)**

*Pre-requisites:*Graduate Student Status

**Outcomes**

Students will be able to: analyze limits and continuity for complex functions; evaluate contour integrals (by the fundamental theorem, by Cauchy integral formula, and by the residue theorem); and represent functions as Laurent series, classifying singularities and poles**MATH 454**

**Survey of Analysis**

**(3 Credit Hours)**

*Pre-requisites:*Graduate Student status

**Outcomes**

Students will understand the central elements of Lebesgue integration (from measurable sets to the fundamental theorem of calculus for Lebesgue integrals) and of Lp spaces (including Minkowski and Hölder inequalities)**MATH 456**

**Introduction to Mathematical Modeling**

**(3 Credit Hours)**

**MATH 458**

**Topics in Optimization**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH458/STAT458/428

**MATH 460**

**Theory of Games**

**(3 Credit Hours)**

**MATH 464L**

**History of Math with Science Contributions for Middle Grades**

**(3 Credit Hours)**

**Outcomes**

Students will obtain a unique historical perspective on the various areas of mathematics in the middle grades**MATH 465**

**Introduction to Partial Differential Equations**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH465/STAT465

**MATH 466L**

**Geometry with Science Applications for the Middle Grades**

**(3 Credit Hours)**

*Pre-requisites:*This course is limited to graduate education students only; it is not accepted for other Mathematics and Statistics graduate degree programs

**MATH 468L**

**Probability and Statistics with Science Applications for Middle Grades**

**(3 Credit Hours)**

*Pre-requisites:*School of Education Graduate Program

**Outcomes**

Students will obtain a background in the fundamentals of descriptive and inferential statistics**MATH 469L**

**Mathematics and Science Applications for Middle Grades**

**(3 Credit Hours)**

**Outcomes**

Students will acquire knowledge of mathematics that supports scientific investigation for the middle grades**MATH 475**

**Functional Analysis**

**(3 Credit Hours)**

**MATH 476**

**Automata & Formal Languages**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP476/MATH476

**MATH 486**

**General Topology**

**(3 Credit Hours)**

**MATH 488**

**Special Topics in Mathematics**

**(1-4 Credit Hours)**

**MATH 495**

**Graduate Practicum in Mathematics**

**(2 Credit Hours)**

*Pre-requisites:*MATH 401 and (MATH 414 or MATH 452 or MATH 416 or MATH 454); Graduate Student status

**Outcomes**

Students will have: analyzed professional literature from multiple sources, resulting in a motivating question for the project; gained practice communicating clearly, concisely, and in-step with discipline norms; and contributed to the learning, teaching, or application of mathematics through their findings**MATH 498**

**Independent Study**

**(1-6 Credit Hours)**

**MATH 595**

**Thesis Supervision**

**(6 Credit Hours)**

**MATH 605**

**Master's Study**

**(0 Credit Hours)**

## Statistics (STAT)

**STAT 401**

**Introduction to Applied Statistics Using R**

**(1 Credit Hour)**

*Pre-requisites:*Limited to Graduate Students Only

**Outcomes**

Upon completion of this course, it is expected that students will skillfully and accurately perform real-time data analysis using R and R/Studio**STAT 403**

**SAS Program & Applied Statistics**

**(3 Credit Hours)**

**STAT 404**

**Probability & Statistics I**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH404/STAT404

**STAT 405**

**Probability & Statistics II**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH405/STAT405

**STAT 406**

**Stochastic Processes**

**(3 Credit Hours)**

*Course equivalencies:*X-MATH406/STAT406

**STAT 407**

**Statistical Design**

**(3 Credit Hours)**

**STAT 408**

**Applied Regression Analysis**

**(3 Credit Hours)**

**STAT 410**

**Categorical Data Analysis**

**(3 Credit Hours)**

**STAT 411**

**Applied Survival Analysis**

**(3 Credit Hours)**

**STAT 421**

**Math Modeling & Simulation**

**(3 Credit Hours)**

*Course equivalencies:*X-COMP421/MATH421/STAT421

**STAT 426**

**Advanced Statistical Inference**

**(3 Credit Hours)**

**STAT 436**

**Topics in Biostatistics**

**(3 Credit Hours)**

**STAT 437**

**Quantitative Bioinformatics**

**(3 Credit Hours)**

**STAT 438**

**Introduction to Predictive Analytics**

**(3 Credit Hours)**

*Pre-requisites:*Graduate students only

**Outcomes**

Upon completion of this course, it is expected that students will master applied methods in predictive analytics (using R and/or Python) with applications to real data-sets**STAT 444**

**Longitudinal Data Analysis and Mixed Modeling**

**(3 Credit Hours)**

*Pre-requisites:*Graduate Students only

**Outcomes**

Upon completion of this course, it is expected that students will master applied mixed-modelling methods (using R and/or SAS) with applications to real data-sets**STAT 451**

**Applied Nonparametric Methods**

**(3 Credit Hours)**

*Pre-requisites:*Graduate Students only

**Outcomes**

Upon completion of this course, it is expected that students will master applied nonparametric statistical methods (using R and/or SAS) with applications to real data-sets**STAT 465**

**Actuarial Theory I**

**(0 Credit Hours)**

*Course equivalencies:*X-MATH465/STAT465

**STAT 466**

**Actuarial Theory II**

**(0 Credit Hours)**

*Course equivalencies:*X-STAT466/MATH466

**STAT 468**

**Risk Theory**

**(0 Credit Hours)**

*Course equivalencies:*X-STAT468/MATH468

**STAT 488**

**Topics in Statistics**

**(1-3 Credit Hours)**

**STAT 495**

**Statistical Consulting Capstone**

**(2 Credit Hours)**

*Pre-requisites:*Graduate Students only

**Outcomes**

Upon completion of this course, it is expected that students will master the soft-skills of statistical consulting, communication, active listening, and real-time data analysis**STAT 498**

**Independent Study Statistics**

**(1-6 Credit Hours)**