Skip to content. Skip to main navigation.

avatar

Dr. Esteban Diaz

Name

[Diaz, Dr. Esteban]
  • Lecturer, Department of Mathematics

Research and Expertise

  • Finite Geometries

    My mathematical research is focused on finite geometries. A finite geometry is a triple (P,S,I), where P is a set of elements called points, S is a non empty collection of elements of P whose elements are called lines or blocks and I is the incidence relation of the lines. 

    During my dissertation I worked on the question of what would be the translation plane if we know that the collineation group is of order (q + 1)^2, where q is a power of a prime. I concluded that it is possible to classify the translation planes admitting this group under some conditions over the primitive divisors of q + 1 and the group being Abelian. The translation planes I found are the so called conical flock planes. This was a conjecture proposed fifteen years ago by my advisor, professor Norman Johnson. 

    One pressing question is the generalization of the previous result to the so called non-Abelian groups.

Publications

      Journal Article 2010
      • Elation switching in real parallelisms. Dr. Diaz, Esteban; Johnson, Prof.

        Norman L.; Dr. Montinaro, Alessandro. 

        {Journal Article }

      Journal Article 2009
      • Translation Planes admitting a Linear Abelian Group of order (q + 1)^2. Dr. Diaz, Esteban; Dr. Vega, Oscar. 

        {Peer Reviewed }

      Journal Article 2008
      • Transitive deficiency one partial parallelisms. Dr. Diaz, Esteban; Prof. Johnson,

        Norman L.; Dr. Montinaro, Alessandro. 

        {Journal Article }
      2008
      • Coset switching in parallelisms. Dr. Diaz, Esteban; Prof. Johnson, Norman L.;

        Dr. Montinaro, Alessandro 

        {Journal Article }

Collaborators

    • thumbnail
      Duration : Jan 2000 to Present

Courses

      • MATH 1301-004 CONTEMPORARY MATHEMATICS

        This course covers material in a traditional algebra course together with real-world applications of mathematics. It develops problem-solving and critical thinking skills. Topics include the mathematics of dimensional analysis, mathematical logic, population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. The use of mathematical software and calculators is required. 

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1301-015 CONTEMPORARY MATHEMATICS

        This course covers material in a traditional algebra course together with real-world applications of mathematics. It develops problem-solving and critical thinking skills. Topics include the mathematics of dimensional analysis, mathematical logic, population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. The use of mathematical software and calculators is required. 

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1302-250 COLLEGE ALGEBRA

        This course is designed as preparation for higher level mathematics courses. Topics include the study of linear, quadratic, polynomial, rational, radical, absolute value, logarithmic, and exponential functions, relations and inequalities; graphs, basic characteristics, and operations on functions; real and complex zeros of functions; graphing techniques; systems of equations and matrices. The use of mathematical software and calculators is required. 

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 2326-005 Calculus III

        This course is about functions whose input and/or output consist of more than one variable, and how the ideas of calc 1 and 2 are applied in this more general setting. Prerequisite: C or better in MATH 2425 or Honors Calc 2.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 2425-150 CALCULUS II

        Student Learning Outcomes: Upon completion of Math 2425, the student should be able to:

        1. Compute the area between two curves, in both rectangular and polar coordinates; compute volumes and surface areas of solids of revolution, in both rectangular and polar coordinates; computes arc length of both polar and rectangular curves;

        2. Compute the value of integrals by the method of integration by parts, trigonometric substitution and partial fractions;

        3. Compute the values of improper integrals;

        4. Compute the limits of sequences and series;

        5. Determine the radius of convergence of power series; differentiate and integrate power series;

        6. Represent a known function as a Taylor series; approximate a known function with a Taylor polynomial and determine the error involved;

        7. Justify and explain their steps in problem solving. In particular, students should be able to construct correct and detailed mathematical arguments to justify their claimed solutions to problems.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1426-300 Calculus I

        Student Learning Outcomes:

        Upon completion of Math 1426, the students will be able to perform various tasks including (but not

        limited to) those outlined below with algebraic, trigonometric and transcendental functions.

        1.Students will be able to compute the limit of various functions without the aid of a calculator.

        2.Students will be able to compute the derivatives and differentials of various functions without the aid of a calculator, and interpret certain limits as derivatives. In particular, they will be able to compute derivatives and differentials using differentiation techniques such as chain rule, implicit differentiation and logarithmic differentiation.

        3.Students will be able to find the equation of the tangent line to the graph of a function at a point by using the derivative of the function. They will be able to estimate the value of a function at a point using a tangent line near that point.

        4.Students will be able to sketch the graphs of functions by finding and using first-order and second-order critical points, extrema, and inflection points.

        5. Students will be able to solve word problems involving the rate of change of a quantity or of related quantities. Students will be able to solve optimization problems in the context of real-life situations by using differentiation and critical points of functions. The problem topics include (but are not limited to) population dynamics, finance, physics, biology, chemistry and sociology.

        6.Students will compute the area below the graph of a function by using a limit of a Riemann sum and/or by using a definite integral.

        7.Students will be able to compute certain antiderivatives using various antidifferentiation techniques such as integration by substitution. They will be able to apply the Fundamental Theorems of Calculus to compute derivatives, antiderivatives, definite integrals and area.

        8.Students will be able to justify and explain their steps in problem solving. In particular, students will be able to construct correct and detailed mathematical arguments to justify their claimed solution

      • MATH 2326-001 CALCULUS III

        This course is about functions whose input and/or output consist of more than one variable, and how the ideas of calc 1 and 2 are applied in this more general setting. Prerequisite: C or better in MATH 2425 or Honors Calc 2.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1302-300 COLLEGE ALGEBRA

        This course is designed as preparation for higher level mathematics courses. Topics include the study of
        linear, quadratic, polynomial, rational, radical, absolute value, logarithmic, and exponential functions,
        relations and inequalities; graphs, basic characteristics, and operations on functions; real and complex zeros
        of functions; graphing techniques; systems of equations and matrices. The use of mathematical software
        and calculators is required.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 2425-100 CALCULUS II

        This course includes the study of applications of integration, techniques of integration, parametric equations, polar coordinates, sequences, and series.
        Prerequisite: C or better in MATH 1426 or HONR-SC 1426.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1301-200 CONTEMPORARY MATHEMATICS

        This course covers material in a traditional algebra course together with real-world applications of
        mathematics. It develops problem-solving and critical thinking skills. Topics include the mathematics of
        dimensional analysis, mathematical logic, population growth, optimization, voting theory, number theory,
        graph theory, relations, functions, probability, statistics, and finance. The use of mathematical software and
        calculators is required.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours1 Document
      • MATH 3319-003 DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA

        Ordinary differential equations, vector spaces, linear transformations,

        matrix/vector algebra, eigenvectors, Laplace Transform, and Systems of Equations.

      • MATH 1301-003 Elementary Mathematical Modeling

        This course covers material in a traditional algebra course together with real-world applications of mathematics. It develops problem-solving and critical thinking skills. Topics include the mathematics of dimensional analysis, mathematical logic, population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. The use of mathematical software and calculators is required.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1301-005 Contemporary Mathematics

        This course covers material in a traditional algebra course together with real-world applications of mathematics. It develops problem-solving and critical thinking skills. Topics include the mathematics of dimensional analysis, mathematical logic, population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. The use of mathematical software and calculators is required.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 3321-001 ABSTRACT ALGEBRA I

        We will focus on Chapters I-IV of the book. The topics will include groups, subgroups, permutations, homomorphism, factor groups, introduction to rings and fields. Upon completion of Math 3321, the students should have a solid knowledge of the topics outlined above. In particular, you should be able to: write the definition of most of the terms, solve problems, and construct correct and detailed mathematical arguments to justify your claimed statements.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1421-251 PREPARATION FOR CALCULUS

        Upon completion of Math 1421:

        Students will be able to justify and explain their steps in problem solving. In particular, students will be able to construct correct and detailed mathematical arguments to justify their solutions to problems.

        Students will demonstrate facility with expressing, applying, and combining functions in tabular, graphical, and symbolic forms. 

        Students will be able to identify and analyze the unifying characteristics of functions and their graphs including invariant properties under function transformations, domain and range, asymptotes, zeroes, and end behavior.

        Students will be able to interpret and define the six trigonometric functions, in terms of both right triangles and the unit circle. They will be able to graph trigonometric and inverse trigonometric functions, without the aid of a graphing calculator, by applying the concepts of amplitude, periods and phase shifts. Students will also be able to verify and use trigonometric identities and formulas and to apply them to solve trigonometric equations and word problems, including problems that require solving a triangle. 

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 311-002 Foundations for Contemporary Mathematics

        Over the course of the semester, you will study various fundamental mathematical concepts based on your individual needs. This material will provide a firm foundation for Contemporary Mathematics as well as a variety of future courses and teach you critical thinking and processing skills. Our purpose is to help make you successful in all degree fields!

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1301-004 Contemporary Mathematics

        Over the course of the semester, you will study traditional algebra topics together with real-world applications of mathematics; problem-solving techniques; dimensional analysis and mathematical logic; as well as population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. This is material that will provide a firm foundation for a variety of future courses as well as teach you critical thinking and processing skills. Our purpose is to help make you successful in all degree fields!

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1301-005 Contemporary Mathematics

        Over the course of the semester, you will study traditional algebra topics together with real-world applications of mathematics; problem-solving techniques; dimensional analysis and mathematical logic; as well as population growth, optimization, voting theory, number theory, graph theory, relations, functions, probability, statistics, and finance. This is material that will provide a firm foundation for a variety of future courses as well as teach you critical thinking and processing skills. Our purpose is to help make you successful in all degree fields!

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1302-300 COLLEGE ALGEBRA

        Over the course of the semester, you will study linear, quadratic, polynomial, rational, radical, absolute value, logarithmic, and exponential functions and their graphs; characteristics of other basic functions, graphing techniques, and operations on functions; systems of equations; and matrices. This is material that will provide a firm foundation for a variety of future courses as well as teach you critical thinking and processing skills. Our purpose is to help make you successful in all degree fields!

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1302-350 COLLEGE ALGEBRA

        Over the course of the semester, you will study linear, quadratic, polynomial, rational, radical, absolute value, logarithmic, and exponential functions and their graphs; characteristics of other basic functions, graphing techniques, and operations on functions; systems of equations; and matrices. This is material that will provide a firm foundation for a variety of future courses as well as teach you critical thinking and processing skills. Our purpose is to help make you successful in all degree fields!

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours