# Claire Wladis

Professor

Mathematics

EMAIL: cwladis@bmcc.cuny.edu

Office: N-598E

Office Hours: (fall 2017) Tues 9am-12pm

Phone: +1 (212) 220-1363

Claire Wladis works in both mathematics and education research. Her mathematics research is in geometric group theory, where she uses diagrams or other visual representations of groups to look for fundamental properties or interesting behavior in certain classes of groups (the Thompson groups specificallly). Her education research is focused on issues of student success and retention, particularly in mathematics, particularly in online courses, remedial courses, and STEM gateway mathematics courses such as intermediate algebra. She has been teaching online for almost a decade, and is very interested in exploring how technology and collaborative learning can be used to enhance student conceptual understanding in abstract and applied mathematics.

Students can find course information at Prof. Wladis’s webpage at www.cwladis.com/math.

## Expertise

Mathematics Education, Geometry/Topology, Geometric Group Theory , Educational Technology, Educational Policy, Developmental Mathematics Education, Community Colleges

## Degrees

- B.A. Yale University, philosophy,
- M.S. University of Texas at Dallas, mathematical sciences,
- Ph.D. CUNY Graduate Center, mathematics,

## Courses Taught

- This course is a combination of arithmetic and elementary algebra. It includes the arithmetic of integers, fractions, decimals, and percent. In addition, such topics as signed numbers, algebraic representation, operations with polynomials, factoring, the solution of simultaneous linear equations of two variables, and graphing are covered.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course is the first algebra course offered at the College. It includes such topics as algebraic representation, signed numbers, operations with polynomials, factoring, the solution of linear equations, the coordinate system, the solution of simultaneous linear equations of two variables, and graphing. This course is designed to prepare students for the CUNY Freshman Skills Assessment Test required for transfer to the upper division of CUNY, as well as for more advanced math courses. If a student passes MAT 12, the student should not register for MAT 51, since MAT 12 combines MAT 8 and MAT 51.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course is the second algebra course offered at the college. It is open to students who have completed elementary algebra or its equivalent. It includes such topics as: factoring, solutions of linear and quadratic equations, trigonometric relationships, exponents, logarithms, and the graphs of quadratic equations.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course covers computations and measurements essential in the health science professional fields. Topics include: units and measurements, ratios, solutions and dosages.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers basic statistics, including: measures of central tendency, measures of dispersion, graphs, correlation, the regression line, confidence intervals, the significance of differences, and hypothesis testing, including z-tests, t-tests, and chi-square tests.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers fundamental mathematical topics associated with computer information systems, including: numeration systems; sets and logic; Boolean algebra, functions, and elementary switching theory; combinatorics; mathematical induction; permutations; combinations; binomial coefficients; and distributions.

Prerequisite: MAT 12 or MAT 51; and MAT 56 or MAT 56.5 or MAT 206.5.

Course Syllabus - This course covers basic algebraic and trigonometric skills, algebraic equations, and functions. Topics include: mathematical induction, complex numbers, and the binomial theorem.

Prerequisite: MAT 56 or MAT 56.5

Course Syllabus - This is an integrated course in analytic geometry and calculus, applied to functions of a single variable. It covers a study of rectangular coordinates in the plane, equations of conic sections, functions, limits, continuity, related rates, differentiation of algebraic and transcendental functions, Rolle's Theorem, the Mean Value Theorem, maxima and minima, and integration.
Prerequisite: MAT 206 or MAT 206.5

Course Syllabus - This course provides an introduction to the concepts of formal integration. It covers the differentiation and integration of algebraic, trigonometric, and transcendental functions. Topics include the definite integral, the antiderivative, areas, volumes, and the improper integral.
Prerequisite: MAT 301

Course Syllabus - This course is an extension of the concepts of differentiation and integration to functions of two or more variables. Topics include partial differentiation, multiple integration, Taylor series, polar coordinates and the calculus of vectors in one or two dimensions.
Prerequisite: MAT 302

Course Syllabus - This course covers matrices, determinants, systems of linear equations, vector spaces, eigenvalues and eigenvectors, Boolean algebra, switching circuits, Boolean functions, minimal forms, Karnaugh maps.
Prerequisite: MAT 302, or permission of the department

Course Syllabus - This course covers the standard material comprising an introduction to group and ring theory: set theory and mappings; groups, normal subgroups, and quotient groups; Sylow's Theorem; rings, ideals, and quotient rings, Euclidean rings, polynomial rings.
Corequisite: MAT 315

Course Syllabus - This course includes the study of several mathematical systems. The role of mathematics in modern culture, the role of postulational thinking in all of mathematics, and the scientific method are discussed. The course considers topics such as: the nature of axioms, truth and validity; the concept of number; the concept of set; scales of notation; and groups and fields.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus

## Research and Projects

- research on the generalized Thompson groups, specifically subgroup and metric properties
- model of online student retention, and online STEM student retention
- elementary algebra concept inventory

## Publications

- Cyclic Subgroups are Quasi-isometrically Embedded in the Thompson-Stein Groups, International Journal of Algebra and Computation
- Thompson’s group F(n) is not minimally almost convex, New York Journal of Mathematics
- Thompson’s Groups are Distorted in the Thompson-Stein Groups, Pacific Journal of Mathematics
- Unusual geodesics in generalizations of Thompson’s group F, Illinois Journal of Mathematics
- The word problem and the metric for generalizations of Thompson’s group F on more than one integer, Journal of the London Mathematical Society
- Retention at What Cost? Community Colleges and Restrictive Policies in Online Learning (with Alyse Hachey and Kay Conway), Journal of College Student Retention: Research, Theory & Practice
- Evolution of Online Education at a Community College (with Alyse Hachey and Kay Conway), Academic Exchange Quarterly
- Is the Second Time the Charm? Investigating Trends in Online Re-enrollment, Retention and Success (with Alyse Hachey and Kay Conway), The Journal of Educators Online
- The Role of Enrollment Choice in Online Education: Course Selection Rationale and Course Difficulty as Factors Affecting Retention (with Alyse Hachey and Kay Conway) , submitted for publication
- Minority Student Access in the Online Environment (with Alyse Hachey and Kay Conway) , Hispanic Educational Technologies Services (HETs) Journal
- An Analysis of the Effect of the Online Environment on STEM Student Success (with Alyse Hachey and Kay Conway), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education, Mathematical Association of America
- Identifying Developmental Students Who are At-Risk: An Intervention Using Computer-Assisted Instruction at a Large Urban Community College (with Kathleen Offenholley and Michael George), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education, Mathematical Association of America
- Are online students in STEM (Science, Technology, engineering and Mathematics) courses at greater risk of non-success? (with Alyse Hachey and Kay Conway), submitted for publication
- Increasing Student Success in Intermediate Algebra through Collaborative Learning at a Diverse Urban Community College (with Alla Morgulis), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education, Mathematical Association of America

## Honors, Awards and Affiliations

- BMCC/CUNY Title V Research Stipend, 2011

Assessing Online Students at Risk: Building a Better Predictive Model for Online Course Attrition - PSC-CUNY research award, 2004-2005

to support archival research in Stockholm, Moscow and St. Petersburg for a play based on mathematician Sofia Kovalevskaya - AWM-NSF Conference Travel Grant, 2009

New Directions in Geometric Group Theory - BMCC/CUNY Faculty Development Grant, 2009

Homology of the Braided Thompson Groups - Scholar Incentive Award, 2007-2008

Metric Properties and Cryptographic Applications of the Braided Thompson Groups - PSC-CUNY Traditional B Reesearch Award, 2011-2012

Assessing Online Students at Risk: Building a Better Predictive Model for Online Course Attrition - PSC-CUNY Research Award 2009-2010

Metric Properties of Generalizations of Thompson’s Group F - CUNY Improving Undergraduate Mathematics Learning Grant, 2010-2011

Increasing Student Success and Retention in Mathematics through Student-Centered Instruction and Collaborative Learning - Nominated for the Feliks Gross Endowment Award, 2009 and 2010