What Do I Teach?
Extensive Experience!
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I am Ph.D. mathematician with 25 years of experience teaching in universities and many years of experience tutoring students at the middle school, high school, undergraduate, and graduate levels. This includes work with adult returning students.
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Passionate about Teaching,
Passionate about Mathematics!
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I am passionate about helping students learn and think about mathematics and be successful in their courses and on their exams. I am also passionate about mathematics itself. I am happy to provide enrichment to students and am not afraid of challenging problems or topics.
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More to Read!
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Please read the following details about particular courses and topics.
AP Calculus, Calculus I-III,
Business Calculus, Calculus for the Life Sciences
I tutor and teach calculus regularly. I tutor many AP Calculus and college calculus students. I have taught traditional calculus courses (for physics, engineering, and mathematics), calculus courses for life sciences, and business calculus. I have served as a Reader (grader) for the AP Calculus exams. I use graphing calculators, computer algebra systems, and online platforms as needed when teaching and tutoring calculus. I have written a preliminary edition of a rigorous text for students in the life sciences
Additionally, I teach and tutor more advanced related topics including real analysis, complex analysis, and topology.
SAT and ACT Mathematics
I am familiar and proficient with the mathematics content on the SAT and ACT exams, including the new digital format. I regularly tutor all of the topics on these exams. I have taught courses in college algebra, trigonometry, precalculus, elementary algebra, and intermediate algebra. I have regularly taught a geometry course for future high school teachers.
I also have taught and regularly tutor for calculus courses, which provides a broader, contextual viewpoint of how all of this this content in used in later mathematics courses. I am proficient in using graphing calculators in teaching and tutoring any of this content, and practice connecting algebraic (symbolic) approaches to visual (graphical) approaches to help deepen students' understanding.
Algebra I, Algebra II,
Elementary Algebra,
Intermediate Algebra
I tutor in all high school and basic algebra courses. I have worked with middle school students in Algebra I, too.
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I have taught courses in college algebra, trigonometry, intermediate algebra, and elementary algebra. I am proficient using graphing calculators in teaching and tutoring any of this content, and practice connecting algebraic (symbolic) approaches to visual (graphical) approaches to help deepen students' understanding.
Additionally, I also teach and tutor undergraduate and graduate level algebra including linear algebra, group theory, ring theory, field theory, Galois theory, multilinear algebra, modules, homological algebra, and combinatorial group theory.
Ordinary Differential Equations, Partial Differential Equations, Nonlinear Dynamics, Difference Equations
I tutor in ordinary differential equations, partial differential equations, Fourier series, nonlinear dynamics, and difference equations. I also tutor in mathematical biology.
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I have taught courses with significant differential equations content. My research in mathematical biology has used systems of differential equations and difference equations.
Modern Geometry, Non-Euclidean Geometry, Differential Geometry,
Topology
In addition to tutoring high school geometry, I tutor in advanced undergraduate and graduate-level in geometry and topology. This is includes courses called Modern Geometry, Advanced Euclidean Geometry, Non-Euclidean Geometry, Hyperbolic Geometry, Differential Geometry, Transformation Groups, General Topology, Algebraic Topology, and Differential Topology.
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I have taught a geometry course for future high school teachers and other mathematics majors and a geometry course for future elementary school teachers. This course, with a strong emphasis on non-Euclidean geometry, integrated algebraic and analytic approaches to studying geometry. I am proficient in the geometry software GeoGebra and Cinderella.
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I have also taught courses in knot theory, differential, general topology, and algebraic topology.
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My Ph.D. research area of hyperbolic three-manifolds and Kleinian groups, is at the intersection of hyperbolic geometry, low-dimensional topology, and complex analysis.
AP Statistics, Introductory Statistics,
Probability and Statistics
I have tutored many students in various statistics courses, including AP Statistics, college level statistics courses, and advanced college level probability and statistics courses. I am fluent in using TI graphing calculators for statistics, which is particularly helpful for AP Statistics.
Geometry
I tutor high school geometry students and students college and graduate-level courses. I have tutored middle school students in high school geometry, too.
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I have taught a geometry course for future high school teachers and other mathematics majors and a geometry for future elementary school teachers. My Ph.D. research area is a very geometric area of mathematics. I am proficient with several dynamic geometry software packages including GeoGebra and Cinderella.
Additionally, I teach and tutor in modern geometry, hyperbolic geometry, differential geometry, low-dimensional topology, algebraic topology, transformation groups, and complex analysis.
College Algebra, Trigonometry, Precalculus, AP Precalculus
I tutor in all versions of college algebra, finite mathematics, trigonometry, and precalculus. This includes the AP Precalculus course.
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I have taught courses each of these areas. I also regularly tutor in and have taught calculus courses, which provides a broader, contextual viewpoint of how this content in used in later mathematics courses. I am proficient in graphing calculators in teaching and tutoring any of this content, and practice connecting algebraic (symbolic) approaches to visual (graphical) approaches to help deepen students' understanding.
Linear Algebra
I tutor students in linear algebra.
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I have also taught linear algebra and used linear algebra in my research work. Linear algebra has applications to many areas in and outside of mathematics and can be a gateway for learning how to write mathematical proofs.
Discrete Mathematics, Combinatorics, Graph Theory
I tutor students in discrete mathematics, combinatorics, and graph theory.
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I have also taught an advanced undergraduate applied combinatorics course with a strong focus on graph theory.