GUIDING PRINCIPLES

1. Students will demonstrate familiarity with the principal definitions and theorems of primary areas of mathematics.  
   1. Students will demonstrate an appreciation of the role of precise definitions and formal mathematical structures in mathematical argument. 
   2. Students will understand the basic nature of proof in mathematics, by a) being able to recognize a valid mathematical proof and b) being able to construct valid mathematical proofs and arguments.
2. Students will develop quantitative problem-solving skills and cultivate facility with and appreciation for mathematical and statistical thinking and expression.  
   1. Students will demonstrate understanding of and facility with mathematical computations, algorithms, and problem-solving strategies. 
   2. Students will develop and demonstrate the ability to communicate mathematical material, both a) in written form and b) orally.
3. Students will be able to utilize the power of mathematical vocabulary, abstract tools, and computational techniques in the formulation and analysis of appropriate problems across subdisciplinary boundaries within mathematics, in other portions of the curriculum, and in real-world situations. 
   1. Students will be able to complete a) basic problems as well as b) longer, connected problems requiring synthesis. 
   2. Students will be able to solve “word problems” by applying mathematical thought to various contexts and recognizing connections between mathematics/statistics and the outside world.  
   3. Students will be able to apply technology appropriately to quantitative problems. 
   4. Students will develop an appreciation for mathematical utility, beauty and elegance.

1. Students will be able to apply the most commonly used statistical methods, including those used in data science and other domains.  
   1. Students will be able to explain and implement the data collection process, including the role of statistics in sample surveys, experiments, and observational studies.
   2. Students will be able to apply statistical thinking to identify issues of bias and confounding when reading or analyzing studies.
   3. Students will be able to determine appropriate estimation, testing, and other inferential methods for one-sample, two-sample, and regression/ANOVA problems.
   4. Students will be able to identify the limitations of the most commonly used statistical methods and be able to recognize situations where these methods do not apply.
2. Students will be competent users of R for statistical programming and data science. 
   1. Students will be able to use R to read in data, create appropriate numerical summaries and data visualizations, and manipulate data to create new variables or data sets as needed.
   2. Students will know how to use R packages, how to debug code, and how to resolve coding difficulties through internet searches and use of the R documentation.
3. Students will have a working knowledge of probability, statistical theory and related mathematics.
   1. Students will be able to solve problems in calculus and applied linear/matrix algebra. 
   2. Students will be able to solve problems in probability and the theory of statistical inference.  
4. Students will be able to communicate the results of data analyses both orally and in written form. 

As an Augustinian Catholic university, we at Villanova believe that diversity of all kinds is at the heart of teaching and learning experiences. Whether student, staff, or faculty member, we know that to grow is to broaden perspectives and develop new insights on the world.

The faculty of the Department of Mathematics and Statistics are committed to promoting UNITAS in support of the mission of both the University and the College of Liberal Arts and Sciences.

The Department of Mathematics and Statistics values, embraces, and celebrates diversity in our student, faculty and staff populations. We strive to create a community built upon mutual respect, inclusive practices, and overall equity. We recognize and value the perspectives of individuals across all races, genders, abilities, orientations, identities, socioeconomic groups, faiths, cultures and other backgrounds.

These perspectives bring a wealth of ideas and experiences to bear on our classes, our disciplines and the functioning of our Department. Thus, we are committed to enhancing UNITAS in our Department and our curriculum.

We are also committed to listening, to learning, and to implementing new strategies within our Department to encourage and assist all community members in their ability to explore, grow, and flourish. We seek to remove cultural and systemic barriers and other obstacles to full representation of, and participation by, people from underrepresented groups, especially women and people of color, particularly in the highest ranks of our faculty.

We recognize that our actions at the Departmental level have an impact on the climate of the University and society at large, and we use this knowledge to motivate and guide our efforts.