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Karl Backs

Name

[Backs, Karl]

Publications

      Journal Article 2015
      • Karl Backs, Steve Jackson, R. Daniel Mauldin, CH, V=L , disintegration of measures, and {\Pi}^1_1 sets, Advances in Mathematics, Volume 274, 9 April 2015, Pages 76-96.

        {Peer Reviewed }

Courses

      • MATH 1301-009 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours1 Document
      • MATH 1421-100 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1421-200 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 3300-001 INTRODUCTION TO PROOFS

        Techniques for constructing proofs for various propositions. The propositions chosen exhibit properties of functions, relations, sets, cardinality, and other ideas in mathematics. An axiomatic approach to some areas in mathematics. Oral presentations of proofs are required. Prerequisite: Math major or math intended major. C or better in MATH 2425 or HONR-SC 2425.

        Fall - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 3300-001 INTRODUCTION TO PROOFS

        Techniques for constructing proofs for various propositions. The propositions chosen exhibit properties of functions, relations, sets, cardinality, and other ideas in mathematics. An axiomatic approach to some areas in mathematics. Oral presentations of proofs are required. Prerequisite: Math major or math intended major. C or better in MATH 2425 or HONR-SC 2425.

      • 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.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1421-100 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 1421-200 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • MATH 3330-005 Introduction to Matrices and Linear Algebra

        Solving systems of linear equations, matrix operations, determinants, vector spaces, linear transformation, orthogonality, Gram-Schmidt process, projections, and eigenvalues and eigenvectors.

        Spring - Regular Academic Session - 2018 Download Syllabus Contact info & Office Hours
      • 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours1 Document
      • MATH 1301-009 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours1 Document
      • MATH 1421-100 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Fall - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1421-150 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Fall - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 3300-001 INTRODUCTION TO PROOFS

        Techniques for constructing proofs for various propositions. The propositions chosen exhibit properties of functions, relations, sets, cardinality, and other ideas in mathematics. An axiomatic approach to some areas in mathematics. Oral presentations of proofs are required. Prerequisite: Math major or math intended major. C or better in MATH 2425 or HONR-SC 2425.

      • MATH 1301-006 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1421-100 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1421-200 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Spring - Regular Academic Session - 2017 Download Syllabus Contact info & Office Hours
      • MATH 1301-009 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1421-150 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections. Prerequisite: C or better in MATH 1301 or MATH 1302 or MATH 1315, or a qualifying score on Math Placement Test.

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1426-700 Calculus I

        Concepts of limit, continuity, differentiation and integration; applications of these concepts. Prerequisite: A qualifying score on the Math Placement Test (MPT) is required to register for this course.

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 3300-001 INTRODUCTION TO PROOFS

        Techniques for constructing proofs for various propositions. The propositions chosen exhibit properties of functions, relations, sets, cardinality, and other ideas in mathematics. An axiomatic approach to some areas in mathematics. Oral presentations of proofs are required. Prerequisite: Math major or math intended major. C or better in MATH 2425 or HONR-SC 2425.

        Fall - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 3314-001 DISCRETE MATHEMATICS

        An introduction into discrete structures. Propositional calculus, sets and operations, functions, induction, counting, relations and matrices, equivalences and partial orders, graphs and shortest path algorithms, trees and minimal spanning trees, tree traversal, elements of boolean algebra. Prerequisite: C or better in MATH 1426 or HONR-SC 1426.

      • 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.

        Spring - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours1 Document
      • MATH 1301-006 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.

        Spring - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours1 Document
      • MATH 1421-400 Preparation for Calculus

        This course integrates and builds upon concepts and skills from college algebra and trigonometry that are essential to success in calculus. Problem solving activities form the basis for the establishment of these mathematical connections.

        Spring - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1426-400 Calculus I

        Concepts of limit, continuity, differentiation and integration; applications of these concepts.

        Spring - Regular Academic Session - 2016 Download Syllabus Contact info & Office Hours
      • MATH 1426-200 CALCULUS I

        Concepts of limit, continuity, differentiation and integration; applications of these concepts.

        Fall - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 1301-001 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. See course syllabus for details.

        Fall - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 1301-002 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. See course syllabus for details.

        Fall - Regular Academic Session - 2015 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. See course syllabus for details.

        Fall - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 2425-100 Calculus II

        Applications of integration, techniques of integration, parametric equations, polar coordinates, sequences, series, vectors, dot product, cross product, planes and quadric surfaces. Prerequisite: C or better in MATH 1426 or HONR-SC 1426.

      • MATH 1301-003 Contemporary Mathematics

        Intended for Liberal Arts majors. This course will survey real-world applications of mathematics. Topics may include the mathematics of dimensional analysis, population growth, optimization, voting theory, graph theory, networks, probability, statistics, and finance. Credit may be received for only one of MATH 1301, MATH 1302, or MATH 1315. 

        Spring - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 1331-003 Geometrical Inference and Reasoning

        This course is designed to prepare future elementary school teachers mathematically to teach math (as opposed to pedagogically, which is the goal of ECED/BEEP 4311 and EDML 4372). It does this in two main ways: by teaching math which is relevant (not identical) to the math they will be teaching, and by modeling a math classroom through problem-solving activities, cooperative groups, and holding students responsible for deciding (reasoning) what is correct. Basics of geometry, constructions, polygons, tessellations, polyhedra, symmetry, rigid motion, and measurement are the topics that will be studied.

        Spring - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 3319-001 Differential Equations and Linear Algebra

        Introductory course with emphasis on solution techniques. Ordinary differential equations, vector spaces, linear transformations, matrix/vector algebra, eigenvectors, Laplace Transform, and systems of equations. Math majors will not receive credit for this course. Prerequisite: C or better in MATH 2326 or concurrent enrollment.

        Spring - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 2425-200 Calculus II

        This course includes the study of applications and techniques of integration, parametric equations, polar coordinates, sequences, series, vectors, dot products, cross products planes and quadratic surfaces.

        Spring - Regular Academic Session - 2015 Download Syllabus Contact info & Office Hours
      • MATH 1301-003 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2014 Download Syllabus Contact info & Office Hours
      • MATH 1301-008 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. See course syllabus for details. Credit may be received for only one of MATH 1301MATH 1302, or MATH 1315.

        Fall - Regular Academic Session - 2014 Download Syllabus Contact info & Office Hours
      • MATH 2326-003 CALCULUS III

        Vectors, dot product, cross product, planes, quadric surfaces, partial differentiation, multiple integrals (with applications), line integrals, Greens Theorem, surface integrals, Stokes Theorem, divergence theorem. Prerequisite: C or better in MATH 2425 or HONR-SC 2425.

        Fall - Regular Academic Session - 2014 Download Syllabus Contact info & Office Hours
      • MATH 2425-100 CALCULUS II

        Applications of integration, techniques of integration, parametric equations, polar coordinates, sequences, and series. Prerequisite: C or better in MATH 1426 or HONR-SC 1426.

        Fall - Regular Academic Session - 2014 Download Syllabus Contact info & Office Hours