Course level:
100
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MATH-103 Mathematical Ideas
Introduction to the power and scope of mathematical ideas by investigating several particular topics. Topics vary among sections. Example of topics include basic mathematical modeling, dynamic geometry, puzzles and recreational mathematics, linear programming, game theory, voting power, legislative representation, and cryptology. Course is intended for first year and sophomore students in the arts, humanities, and social sciences who do not plan to take calculus. Students who have completed a Mathematics course at Gettysburg College may not enroll in Mathematics 103. No prerequisites.
MATH-104 Quantitative Methods
Introduction to equations, graphs and functions, metrices, systems of linear equations and the derivative and its application. Course is designed for students in the social sciences. Students who have completed Mathematics 105-106 or Mathematics 111 may not enroll in Mathematics 104. No prerequisites.
MATH-105 Calculus with Precalculus I
Study of differential and integral calculus with precalculus. Topics include basic algebraic concepts, equations and inequalities, functions, introduction to limits, continuity, the derivative, and the definite integral.
MATH-106 Calculus with Precalculus II
Study of differential and integral calculus with precalculus. Topics include basic algebraic concepts, equations and inequalities, functions, introduction to limits, continuity, the derivative, and the definite integral.
MATH-107 Applied Statistics
Introduction to statistical methods with applications from social, biological, and health sciences. Topics include descriptive statistics, fundamentals of probability theory, probability distributions, hypothesis testing, linear regression and correlation, analysis of categorical data, and analysis of variance. Laboratory work is designed to utilize the computational power of a statistical computer package. Credit cannot be received for both this course and Mathematics 205, Biology 260, Economics 241, and Psychology 205. Three lecture hours and one laboratory session No prerequisites
MATH-108 Mathematical Reasoning
Study of mathematical reasoning. Possible topics include number theory, bases, logic and problem-solving, rational expressions, algebra, straightedge and compass constructions, tessellations, polyhedra, symmetry, statistics, and mathematical models.
MATH-111 Calculus I
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences. No prior experience with calculus is assumed. Students who have received credit for Mathematics 105-106 cannot also receive credit for Mathematics 111. These students may register for Mathematics 112.
MATH-111 Calculus I (Honors)
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences. No prior experience with calculus is assumed. Students who have received credit for Mathematics 105-106 cannot also receive credit for Mathematics 111. These students may register for Mathematics 112.
MATH-112 Calculus II
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences.
MATH-112 Calculus II (Honors)
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences.
MATH-201 Introduction to Research in Mathematics
Introduction to the methodology and procedures of research in mathematics. After selecting one or more of the open-ended research projects discussed in class, students will individually or in small groups carry out an investigation, culminating in a written report and its public presentation.
MATH-205 Introduction to Statistics
Introduction to descriptive and inferential statistical methods with applications in psychology. Laboratory work involves the use of a computer software package that allows for the application of statistical procedures. Credit may not be granted for this course and Mathematics 107, Biology 260, or Economics 241 Prerequisite: High school algebra. Elementary education students should enroll in Math 205. Required of all majors in Psychology; open only to declared Psychology majors. Three class hours and three laboratory hours.
MATH-211 Multivariable Calculus
Vectors, vector functions, functions of several variables, partial differentiation, optimization, multiple integration, transformation of coordinates, line and surface integrals, and Green's and Stokes' theorems.
MATH-212 Linear Algebra
Systems of linear equations, algebra of matrices, determinants, abstract vector spaces, linear transformations, eigenvalues, and quadratic forms.
MATH-215 Abstract Mathematics I
Introduction to abstract mathematical thinking, emphasizing mathematical reasoning and exposition. Students study elementary logic and basic set theory with rigorous definitions and proofs. This foundation is then used to explore one of several optional topics chosen by the instructor.
MATH-217 Inquisitive Problem Solving
Immersion in the arts of mathematical problem solving and posing, building to the Olympiad and Putnam levels. Possible topics include the use of the pigeonhole principle, proof by induction, applications of invariants, and applications of geometric series in problem posing and solving
MATH-225 Differential Equations
Equations Analysis of one- and two-dimensional differential equations, with an emphasis on the qualitative behavior of solutions. Topics include graphical exploration, numerical approximation, separable and linear equations, phase line and phase plane analysis, conservative and dissipative systems, linearization, and applications to biology, chemistry, and physics.
MATH-301 Intermediate Research in Mathematics
Development of intermediate level research in mathematics. After selecting one or more of the open-ended research projects discussed in class, students will individually or in small groups carry out an investigation which provides a careful and complete proof of their results. The research will culminate in a written report and its public presentation.
MATH-308 Introduction to Combinatorics
Topics selected from partition and permutation theory, enumeration, recursion, partially ordered sets, Markov chains, generating functions, algebraic combinatorics, combinatorial geometry, and design and coding theory. Applications are chosen from computer science, optimization, and the social and life sciences.
MATH-309 Introduction to Graph Theory
Topics are selected from extremal graph theory, network flow and design, coloring, Ramsey theory, matching and transversal theory, random graphs, and algebraic and topological graph theory. Applications are chosen from computer science, optimization, and the social and life sciences
MATH-314 From Zero to Infinity: Philosophical Revolutions in Mathematics
Study of the philosophical foundations of mathematics starting with the concept of number and culminating the Godel's groundbreaking incompleteness result. Specific topics include the historical developments and mathematical and philosophical ramifications of zero, rational, irrational, imaginary, and transfinite numbers as well as an examination of the completeness of arithmetic.
MATH-315 Abstract Mathematics II
Further development of the skills of abstract mathematical reasoning and writing proofs. Course is grounded in a particular subject area chosen by the instructor. Possible areas include topology, number theory, and combinatorics. Not offered every year
MATH-321 Real Analysis
Rigorous treatment of concepts studied in elementary calculus and an introduction to more advanced topics in analysis. Topics include elements of logic and set theory, properties of real numbers, elements of metric space topology, continuity, the derivative, the Riemann integral, sequences and series, and uniform convergence.
MATH-331 Abstract Algebra
Study of basic structures of modern abstract algebra, including groups, rings, fields, and vector spaces.
MATH-337 Number Theory
Study of topics in elementary number theory. Topics include factorization and the prime numbers, Diophantine equations, quadratic reciprocity, and the Fundamental Theorem of Arithmetic. Applications of these ideas to cryptography are explored.
MATH-342 Applied Linear Algebra
Rigorous continuation of first-semester linear algebra, with applications both within mathematics and to the social and natural sciences. Topics, chosen by the instructor, may include matrix powers and exponentials, positive matrices and Markov chains, coding theory, design theory, graph theory, and max-plus algebra.
MATH-343 Topics in Geometry
Study of both synthetic and analytic approaches to geometry. Topics include axiomatic systems, Euclidean geometry, non-Euclidean geometries, projective geometry, and subgeometries of projective geometry.
MATH-351 Mathematical Probability
Combinatorics, discrete and continuous random variables and their distributions, expected value and variance, functions of random variables, the Law of Large Numbers, the Central Limit Theorem, generating functions, and applications such as Markov chains, random walks, and games of chance.
MATH-352 Mathematical Statistics
Expectation, special probability distributions and densities, bivariate and multivariate distributions, sampling distributions, theory and applications of estimation, hypothesis testing, regression, correlation, analysis of variance, and nonparametic methods
MATH-353 Probability and Statistics
Study of topics in probability and statistics. Topics include discrete and continuous random variables and their distributions, expected value and variance, the Law of Large Numbers, the Central Limit Theorem, sampling distributions, theory and application of estimation, hypothesis testing, regression, correlation, and analysis of variance. Applications to problems in the social and natural sciences will also be considered.
MATH-361 Chaos and Dynamical Systems
Dynamical systems and chaos theory. Topics will include linear and nonlinear systems, mappings and orbits, bifurcations, stability theory and applications of dynamical systems.
MATH-362 Operations Research
Study of techniques and tools used in mathematical models applied to the biological and social sciences. Topics are selected from optimization, linear and nonlinear programming, transportation problems, network analysis, dynamic programming, and game theory.
MATH-363 Differential Equations
Equations Analysis of one- and two-dimensional differential equations, with an emphasis on the qualitative behavior of solutions. Topics include graphical exploration, numerical approximation, separable and linear equations, phase line and phase plane analysis, conservative and dissipative systems, linearization, and applications to biology, chemistry, and physics.
MATH-364 Complex Analysis
Complex numbers, analytic functions, complex integration, Cauchy's Theorem, Taylor and Laurent series, contour integrals, the residue theorem, and conformal mapping. .
MATH-366 Numerical Analysis
Numerical techniques for solving mathematical problems. Topics include solutions of equations, solutions of simultaneous linear equations, interpolation and approximation, numerical differentiation and integration, the eigenvalue problem, numerical solutions of ordinary differential equations, and error analysis.
MATH-381 Selected Topics
Study of an advanced phase of mathematics not otherwise in the curriculum. Subject matter and frequency of offering depend on student interest. Possible areas for study are point set topology, combinatorics, graph theory, partial differential equations, differential geometry, and number theory. Prerequisite: Depends on the topic
MATH-401 Advanced Research in Mathematics
Development of advanced level research in mathematics. Students work on open-ended research projects that they have previously worked on in Math 301 (Intermediate Research in Mathematics). The emphasis in this course is on developing professional writing and presentation skills. The goal of the course is for students to complete a formal paper on their research, including an abstract, an overview of the history of the project, a statement of new results, an explanation of methods, a description of possible questions for future research, and a complete bibliography. Students are also expected to present their research off campus.
MATH-403 Senior Thesis
Capstone experience for mathematics majors. Each student explores a topic in significant depth, writes a major paper on the topic, and presents a talk on the topic to mathematics students and faculty. Students meet regularly to discuss course readings, research methods, and their recent individual research findings.
MATH-450 Individualized Study-Tutorial
Individualized tutorial counting toward the minimum requirements in a major or minor, graded A-F
MATH-452 Individualized Study-Tutorial
Individualized tutorial not counting in the minimum requirements in a major or minor, graded A-F
MATH-460 Individualized Study-Research
Individualized research counting toward the minimum requirements in a major or minor, graded A-F
MATH-475 Summer Internship
Summer Internship graded S/U, counting in the mimimum requirements for a major or minor only with written permission filed in the Registrar's Office
MATH-103 Mathematical Ideas
Introduction to the power and scope of mathematical ideas by investigating several particular topics. Topics vary among sections. Example of topics include basic mathematical modeling, dynamic geometry, puzzles and recreational mathematics, linear programming, game theory, voting power, legislative representation, and cryptology. Course is intended for first year and sophomore students in the arts, humanities, and social sciences who do not plan to take calculus. Students who have completed a Mathematics course at Gettysburg College may not enroll in Mathematics 103. No prerequisites.
MATH-104 Quantitative Methods
Introduction to equations, graphs and functions, metrices, systems of linear equations and the derivative and its application. Course is designed for students in the social sciences. Students who have completed Mathematics 105-106 or Mathematics 111 may not enroll in Mathematics 104. No prerequisites.
MATH-105 Calculus with Precalculus I
Study of differential and integral calculus with precalculus. Topics include basic algebraic concepts, equations and inequalities, functions, introduction to limits, continuity, the derivative, and the definite integral.
MATH-106 Calculus with Precalculus II
Study of differential and integral calculus with precalculus. Topics include basic algebraic concepts, equations and inequalities, functions, introduction to limits, continuity, the derivative, and the definite integral.
MATH-107 Applied Statistics
Introduction to statistical methods with applications from social, biological, and health sciences. Topics include descriptive statistics, fundamentals of probability theory, probability distributions, hypothesis testing, linear regression and correlation, analysis of categorical data, and analysis of variance. Laboratory work is designed to utilize the computational power of a statistical computer package. Credit cannot be received for both this course and Mathematics 205, Biology 260, Economics 241, and Psychology 205. Three lecture hours and one laboratory session No prerequisites
MATH-108 Mathematical Reasoning
Study of mathematical reasoning. Possible topics include number theory, bases, logic and problem-solving, rational expressions, algebra, straightedge and compass constructions, tessellations, polyhedra, symmetry, statistics, and mathematical models.
MATH-111 Calculus I
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences. No prior experience with calculus is assumed. Students who have received credit for Mathematics 105-106 cannot also receive credit for Mathematics 111. These students may register for Mathematics 112.
MATH-111 Calculus I (Honors)
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences. No prior experience with calculus is assumed. Students who have received credit for Mathematics 105-106 cannot also receive credit for Mathematics 111. These students may register for Mathematics 112.
MATH-112 Calculus II
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences.
MATH-112 Calculus II (Honors)
Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral, and series. Applications are drawn from the natural and social sciences.
MATH-201 Introduction to Research in Mathematics
Introduction to the methodology and procedures of research in mathematics. After selecting one or more of the open-ended research projects discussed in class, students will individually or in small groups carry out an investigation, culminating in a written report and its public presentation.
MATH-205 Introduction to Statistics
Introduction to descriptive and inferential statistical methods with applications in psychology. Laboratory work involves the use of a computer software package that allows for the application of statistical procedures. Credit may not be granted for this course and Mathematics 107, Biology 260, or Economics 241 Prerequisite: High school algebra. Elementary education students should enroll in Math 205. Required of all majors in Psychology; open only to declared Psychology majors. Three class hours and three laboratory hours.
MATH-211 Multivariable Calculus
Vectors, vector functions, functions of several variables, partial differentiation, optimization, multiple integration, transformation of coordinates, line and surface integrals, and Green's and Stokes' theorems.
MATH-212 Linear Algebra
Systems of linear equations, algebra of matrices, determinants, abstract vector spaces, linear transformations, eigenvalues, and quadratic forms.
MATH-215 Abstract Mathematics I
Introduction to abstract mathematical thinking, emphasizing mathematical reasoning and exposition. Students study elementary logic and basic set theory with rigorous definitions and proofs. This foundation is then used to explore one of several optional topics chosen by the instructor.
MATH-217 Inquisitive Problem Solving
Immersion in the arts of mathematical problem solving and posing, building to the Olympiad and Putnam levels. Possible topics include the use of the pigeonhole principle, proof by induction, applications of invariants, and applications of geometric series in problem posing and solving
MATH-225 Differential Equations
Equations Analysis of one- and two-dimensional differential equations, with an emphasis on the qualitative behavior of solutions. Topics include graphical exploration, numerical approximation, separable and linear equations, phase line and phase plane analysis, conservative and dissipative systems, linearization, and applications to biology, chemistry, and physics.
MATH-301 Intermediate Research in Mathematics
Development of intermediate level research in mathematics. After selecting one or more of the open-ended research projects discussed in class, students will individually or in small groups carry out an investigation which provides a careful and complete proof of their results. The research will culminate in a written report and its public presentation.
MATH-308 Introduction to Combinatorics
Topics selected from partition and permutation theory, enumeration, recursion, partially ordered sets, Markov chains, generating functions, algebraic combinatorics, combinatorial geometry, and design and coding theory. Applications are chosen from computer science, optimization, and the social and life sciences.
MATH-309 Introduction to Graph Theory
Topics are selected from extremal graph theory, network flow and design, coloring, Ramsey theory, matching and transversal theory, random graphs, and algebraic and topological graph theory. Applications are chosen from computer science, optimization, and the social and life sciences
MATH-314 From Zero to Infinity: Philosophical Revolutions in Mathematics
Study of the philosophical foundations of mathematics starting with the concept of number and culminating the Godel's groundbreaking incompleteness result. Specific topics include the historical developments and mathematical and philosophical ramifications of zero, rational, irrational, imaginary, and transfinite numbers as well as an examination of the completeness of arithmetic.
MATH-315 Abstract Mathematics II
Further development of the skills of abstract mathematical reasoning and writing proofs. Course is grounded in a particular subject area chosen by the instructor. Possible areas include topology, number theory, and combinatorics. Not offered every year
MATH-321 Real Analysis
Rigorous treatment of concepts studied in elementary calculus and an introduction to more advanced topics in analysis. Topics include elements of logic and set theory, properties of real numbers, elements of metric space topology, continuity, the derivative, the Riemann integral, sequences and series, and uniform convergence.
MATH-331 Abstract Algebra
Study of basic structures of modern abstract algebra, including groups, rings, fields, and vector spaces.
MATH-337 Number Theory
Study of topics in elementary number theory. Topics include factorization and the prime numbers, Diophantine equations, quadratic reciprocity, and the Fundamental Theorem of Arithmetic. Applications of these ideas to cryptography are explored.
MATH-342 Applied Linear Algebra
Rigorous continuation of first-semester linear algebra, with applications both within mathematics and to the social and natural sciences. Topics, chosen by the instructor, may include matrix powers and exponentials, positive matrices and Markov chains, coding theory, design theory, graph theory, and max-plus algebra.
MATH-343 Topics in Geometry
Study of both synthetic and analytic approaches to geometry. Topics include axiomatic systems, Euclidean geometry, non-Euclidean geometries, projective geometry, and subgeometries of projective geometry.
MATH-351 Mathematical Probability
Combinatorics, discrete and continuous random variables and their distributions, expected value and variance, functions of random variables, the Law of Large Numbers, the Central Limit Theorem, generating functions, and applications such as Markov chains, random walks, and games of chance.
MATH-352 Mathematical Statistics
Expectation, special probability distributions and densities, bivariate and multivariate distributions, sampling distributions, theory and applications of estimation, hypothesis testing, regression, correlation, analysis of variance, and nonparametic methods
MATH-353 Probability and Statistics
Study of topics in probability and statistics. Topics include discrete and continuous random variables and their distributions, expected value and variance, the Law of Large Numbers, the Central Limit Theorem, sampling distributions, theory and application of estimation, hypothesis testing, regression, correlation, and analysis of variance. Applications to problems in the social and natural sciences will also be considered.
MATH-361 Chaos and Dynamical Systems
Dynamical systems and chaos theory. Topics will include linear and nonlinear systems, mappings and orbits, bifurcations, stability theory and applications of dynamical systems.
MATH-362 Operations Research
Study of techniques and tools used in mathematical models applied to the biological and social sciences. Topics are selected from optimization, linear and nonlinear programming, transportation problems, network analysis, dynamic programming, and game theory.
MATH-363 Differential Equations
Equations Analysis of one- and two-dimensional differential equations, with an emphasis on the qualitative behavior of solutions. Topics include graphical exploration, numerical approximation, separable and linear equations, phase line and phase plane analysis, conservative and dissipative systems, linearization, and applications to biology, chemistry, and physics.
MATH-364 Complex Analysis
Complex numbers, analytic functions, complex integration, Cauchy's Theorem, Taylor and Laurent series, contour integrals, the residue theorem, and conformal mapping. .
MATH-366 Numerical Analysis
Numerical techniques for solving mathematical problems. Topics include solutions of equations, solutions of simultaneous linear equations, interpolation and approximation, numerical differentiation and integration, the eigenvalue problem, numerical solutions of ordinary differential equations, and error analysis.
MATH-381 Selected Topics
Study of an advanced phase of mathematics not otherwise in the curriculum. Subject matter and frequency of offering depend on student interest. Possible areas for study are point set topology, combinatorics, graph theory, partial differential equations, differential geometry, and number theory. Prerequisite: Depends on the topic
MATH-401 Advanced Research in Mathematics
Development of advanced level research in mathematics. Students work on open-ended research projects that they have previously worked on in Math 301 (Intermediate Research in Mathematics). The emphasis in this course is on developing professional writing and presentation skills. The goal of the course is for students to complete a formal paper on their research, including an abstract, an overview of the history of the project, a statement of new results, an explanation of methods, a description of possible questions for future research, and a complete bibliography. Students are also expected to present their research off campus.
MATH-403 Senior Thesis
Capstone experience for mathematics majors. Each student explores a topic in significant depth, writes a major paper on the topic, and presents a talk on the topic to mathematics students and faculty. Students meet regularly to discuss course readings, research methods, and their recent individual research findings.
MATH-450 Individualized Study-Tutorial
Individualized tutorial counting toward the minimum requirements in a major or minor, graded A-F
MATH-452 Individualized Study-Tutorial
Individualized tutorial not counting in the minimum requirements in a major or minor, graded A-F
MATH-460 Individualized Study-Research
Individualized research counting toward the minimum requirements in a major or minor, graded A-F
MATH-475 Summer Internship
Summer Internship graded S/U, counting in the mimimum requirements for a major or minor only with written permission filed in the Registrar's Office
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