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COURSES

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This general education math course develops students' quantitative reasoning skills through geometric exploration and visualization in 2D and 3D. Topics include: Platonic, Archimedean, and Catalan solids, tessellations, and tilings, the Golden Rectangle, continued fractions, fractals, fractal carpets, and dimension, Islamic art patterns, math-art puzzles, and perspective drawing. The work of relevant artists is used to make connections with mathematical and geometric concepts. Dynamic geometry software, vector graphic software, 3D printer, and laser cutter are used to create math-art productions. 

Geometry for

Art & Design

Fall 2020, 2019

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This project-based course provides a historical perspective of the development of mathematics with an emphasis on multicultural perspectives from ancient to modern times. Primary source projects will explore methods of the ancients in comparison to modern times. Primary source projects will explore methods of the ancients in comparison to modern solutions to illustrate mathematics as a product of human effort. Historical development of calculus and other mathematical areas are studied. 

History of Mathematics

Fall 2020, Spring 2019, Fall 2018, Fall 2017

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This course includes systems of linear equations, matrices, vector spaces R  and other spaces), basis, linear independence, linear transformations, eigenvalues and eigenvectors, diagonalization, and applications. Mathematical software such as Sage, Octave, and Maple are used throughout the course. 

Linear Algebra

n

2000 - present

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This course introduces students to an in-depth study of geometric topics beyond those studied at the high school level. Finite geometries, the foundations of Euclidean geometry, non-Euclidean geometries, and advanced constructions are studied in historical context. This course will develop students' logical reasoning and proof-writing skills using the axiomatic method, inductive reasoning, and algebra, among other approaches. Dynamic geometry software, GeoGebra, along with 3D modeling software OpenScad, and 3D printing are used to enhance understanding and illustrate various geometric concepts studied in this course. 

Modern Geometry

Spring 2020, Fall 2018, Spring 2017, 2016

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This course provides a study of vectors and vector calculus in three-space, parameterized curves, functions of several variables, differentiation of functions of several variables, multiple integration, and their applications. Mathematics software such as Maple and CalcPlot3D is used. Students are introduced to 3D design software and 3D printing to illustrate and further understand the theorums studied. 

Multivariable Calculus

2000 - Present

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This course includes limits and continuity, theory and techniques of differentiating and integrating algebraic and transcendental functions, and applications of differentiation. Mathematics software such as Maple is used throughout the course along with graphing calculators, GeoGebra, or Desmos. Students are introduced to 3D design software, Tinkercad, and 3D printing to illustrate and further undestand the theorums studied. 

Single-Variable Calculus

2000 - present

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Other courses taught regularly during years since 2000: Precalculus, Finite Mathematics, Introduction to Statistics. 

Other Courses

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Mentoring

2015 - present

Faculty mentor to undergraduate mathematics majors for capstone Senior Seminar research projects and summer research experiences on advanced mathematical topics. As a mentor, I supervise these projects from conception to completion. Multiple students have presented posters at local conferences. 

  • On the Differential Geometry of Minimal Surfaces and their Applications, Giselle Palacios, SXU Senior Seminar, Spring 2021

  • Lessons in Mathematical 3D Printing: Optical Illusions, Fractal Dimension, and Chaotic Attractors, Ryan Gossett, SXU Senior Seminar, Spring 2021

  • A Different Perspective: Exploring Hyperbolic Geometry, David Villanueva, SXU Senior Seminar, Fall 2020

  • Graph Theory: From Euler to Google, Michal Szlachta, SXU Senior Seminar, Spring 2020

  • Mathematics of Minimal Surfaces as Soap Films and Applications to 3D Printing, Giselle Palacios, SXU NSF-HSI EXPLORE STEM Research Program, Summer 2019

  • General Carpet Fractals and Fractal Dimension, Adrian Marquez-Mata, SXU Senior Seminar, Spring 2019

  • Exploring Knot Theory, Christine Labudiong, SXU Senior Seminar, Fall 2018

  • Visualizations and Models in Non-Euclidean Geometry, Joseph Bailey, SXU Senior Seminar, Spring 2018

  • Business Applications with Lagrange Multipliers and 3D Printing, Marilyn Gellert, SXU Senior Seminar, Spring 2017 

  • The Calculus of Running, Courtney Correa, SXU Senior Seminar, Fall 2016

  • Twenty-Five Point Affine Geometry, Johnathan Burch, SXU Senior Seminar, Fall 2016

  • Soap Films and Minimal Surfaces, Mahmoud Othman, SXU Senior Seminar, Fall 2015

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