Mathematics (MA)

MA 100 -  Quantitative Reasoning  
Credits: 3  

Study of practical arithmetic and geometry, data gathering and analysis, introductory probability and statistics, size and bias in sampling, hypothesis testing, confidence intervals and their use in statistical analysis, linear relationships, interpolation and extrapolation, correlation, linear and exponential growth with practical applications.

Prerequisites: Placement by department or permission of instructor.   
Note(s): This course is primarily intended to fulfill the first part of the Quantitative Reasoning requirement, QR1.  
MA 102 -  Mathematical Models in the Social and Management Sciences  
Credits: 3  

In many areas of the social and management sciences, mathematics can be used to make predictions, help allocate scarce resources, maximize profits, make policy decisions, and so on. This use of mathematics is called mathematical modeling. In this course we investigate a variety of scenarios which can arise in the "real world" where math modeling can come into play, and we learn about some of the most important techniques of math modeling such as linear programming, probability theory, statistical techniques, integer programming, and Markov chains.

Note(s): Course offered periodically, depending on faculty availability. Fulfills QR2 requirement.  
MA 107 -  Concepts of Mathematics  
Credits: 3  

An introductory course for liberal arts and education majors or anyone seeking a general, nontechnical overview of mathematics. Topics covered include set theory, review of number systems, geometry concepts, basic concerns of probability and statistics, and introductory number theory.

Note(s): Offered periodically depending on faculty availability. Fulfills QR2 requirement.  
MA 108 -  Calculus with Algebra I  
Credits: 3  

An introduction to derivatives, integrals, and their applications. Primarily for students who are not adequately prepared for MA 111, this course (together with MA 109) covers the same material as MA 111 but integrates the material requisite to calculus with the calculus itself. Note that MA 108 alone cannot be used as a substitute for MA 111. Successful completion of MA 108 and MA 109 is equivalent to completion of MA 111.

Prerequisites: QR1 or MA 100 or placement at the FQR level or placement at the AQR level   
Note(s): Offered fall semester.  
MA 109 -  Calculus with Algebra II  
Credits: 3  

A continuation of MA 108. A study of exponential, logarithmic, and trigonometric functions and their applications in differential and integral calculus. Successful completion of MA 108 and MA 109 is equivalent to completion of MA 111.

Prerequisites: MA 108.   
Note(s): Offered spring semester. Fulfills QR2 requirement; fulfills Fundamental QR requirement.  
MA 110 -  Mathematics Toolkit  
Credits: 2  

A detailed study of the mathematical tools necessary for success in calculus and statistics courses. Students will examine concepts from symbolic, graphical, and numerical perspectives. Concepts covered include polynomial, rational, exponential, logarithmic, and trigonometric functions, and introductory probability and statistics.

Prerequisites: MA 100 or placement into an FQR or AQR course.   
Note(s): Fulfills Fundamental QR requirement.  
MA 111 -  Calculus I  
Credits: 4  

Derivatives, integrals and their applications. Techniques of differentiation. Integration and differentiation of exponential, logarithmic and trigonometric functions.

Prerequisites: High school preparation including trigonometry. Requires AQR placement.   
Note(s): Fulfills QR2 requirement.  
MA 111H -  Honors:Calculus I  
Credits: 4  
MA 113 -  Calculus II  
Credits: 4  

Inverse trigonometric functions and hyperbolic functions. Systematic study of integration. Parametric Equations, polar coordinates and conic sections. Indeterminate forms, L'Hôpital's rule and improper integrals.

Prerequisites: Calculus placement exam, or MA 111, or both MA 108 and MA 109. Requires AQR placement.   
Note(s): Fulfills QR2 requirement.  
MA 113H -  Honors:Calculus II  
Credits: 4  

Inverse trigonometric functions and hyperbolic functions. Systematic study of integration. Parametric Equations, polar coordinates and conic sections. Indeterminate forms, L'Hôpital's rule and improper integrals.

Prerequisites: Calculus placement exam, or MA 111, or both MA 108 and MA 109. Requires AQR placement. (Fulfills QR2 requirement).  
MA 116 -  Math in the Museum  
Credits: 2  

An examination of how mathematical ideas are embodied in the visual arts, architecture, and design, and how the arts have helped shaped advances in math and computer science.  From ancient Greek art to the Renaissance, and from Islamic patterns to contemporary computer-generated art, math has an important place in the world of art, architecture, and design both within museum spaces and all around us. Students will  explore these relationships in the context of mathematical concepts such as geometry, proportion, basic statistics, measurements, and common functions by studying original works of art and actively engaging with these mathematical concepts through hands on exercises in Skidmore's Tang Teaching Museum.

Prerequisites: QR1 or MA 100 or placement at the FQR level or placement at the AQR level.   
Note(s): Letter grade only. Fulfills Fundamental QR requirement.  
MA 125 -  Problem Solving in Mathematics  
Credits: 1  

Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

Prerequisites: QR1.   
Note(s): During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. May be repeated for credit. Must be taken S/U.  
MA 125H -  Honors: Problem Solving In Mathematics (Fr)  
Credits: 1  

Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 126H -  Honors: Problem Solving  
Credits: 1  

Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 200 -  Linear Algebra  
Credits: 4  

Vector spaces, matrices and linear transformations, determinants, solution of linear equations.

Prerequisites: High school preparation including trigonometry.  Requires AQR placement.   
Note(s): Fulfills QR2 requirement.  
MA 202 -  Calculus III  
Credits: 4  

Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, and line integrals.

Prerequisites: MA 113  or calculus placement exam.  
MA 204 -  Probability and Statistics  
Credits: 3  

Elementary probability, discrete and continuous random variables, theory of expectation, analysis of distribution functions.

Prerequisites: MA 111, or both MA 108 and MA 109.   
Note(s): Normally offered spring term of odd-numbered years. Fulfills QR2 requirement.  
MA 211 -  Calculus III  
Credits: 3  

Sequences and Series.  Introduction to multivariable calculus. Taylor Series of a function. Topics include vector functions, partial derivatives, gradients.

Prerequisites: MA 113 or calculus placement exam.   
MA 213 -  Calculus IV  
Credits: 3  

Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, line integrals, surface integrals, vector calculus, divergence and curl.

Prerequisites: MA 211 or MA 202 or permission of instructor.   
MA 214 -  Theory of Numbers  
Credits: 3  

Topics in classical and modern number theory including congruences, Diophantine equations, quadratic residues.

Prerequisites: MA 111, or both MA 108 and MA 109, or MA 200.  Requires AQR placement.   
Note(s): Normally offered spring semester of even-numbered years. Fulfills QR2 requirement.  
MA 215 -  Introduction to Mathematical Reasoning and Proof  
Credits: 4  

An introduction to mathematical proof and concepts of abstract mathematics, including elementary logic, methods of proof, set theory, functions and relations.

Prerequisites: CS 106 or MA 113 or permission of the department.   
Note(s): Fulfills QR2 requirement.  
MA 225 -  Problem Solving In Mathematics  
Credits: 1  

Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

Prerequisites: QR2.   
Note(s): During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. May be repeated for credit. Must be taken S/U.  
MA 225H -  Honors: Problem Solving In Mathematics (So)  
Credits: 1  

Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 226H -  Honors: Problem Solving  
Credits: 1  

Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 251A-D -  Selected Topics in Mathematics  
Credits: 1-4  

Topics that complement the established lower level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.

Prerequisites: QR1.   
Note(s): May be repeated for credit. Offered on sufficient demand.  
MA 270 -  Differential Equations  
Credits: 4  

An introduction to the theory and applications of differential equations.

Prerequisites: MA 113 and MA 200.  
MA 275H -  Research Topics in Mathematics  
Credits: 1  

Exploration of a research topic in mathematics. The students, in collaboration with a faculty mentor, will participate in a research project in a particular area of mathematics which may be related to the faculty member's research program.

Prerequisites: Permission of instructor.  
MA 302 -  Graph Theory  
Credits: 3  

An introduction to the theory and applications of graphs. Topics may include graphs and digraphs, connectivity, trees, Euler and Hamiltonian cycles, and graph embeddings.

Prerequisites: MA 215.   
Note(s): Normally offered fall semester of odd-numbered years.  
MA 303 -  Introduction to Analysis  
Credits: 4  

Rigorous treatment of foundational issues in analysis. Topics may include set theory, the real number system, sequences, series, limits and continuity, theory of differentiation and integration, and elementary notions of topology.

Prerequisites: MA 113 and MA 215.   
Note(s): Offered every semester.  
MA 309 -  Elements of Modern Geometry  
Credits: 3  

Study of various topics in modern geometry, with emphasis on the axiomatic method.

Prerequisites: MA 113 and MA 215.   
Note(s): Normally offered fall semester of even-numbered years. May be repeated for credit with a different topic.  
MA 310 -  History of Mathematics  
Credits: 3  

Study of the development of mathematical ideas.

Prerequisites: MA 113 and MA 215.   
Note(s): Normally offered spring semester of odd-numbered years.  
MA 311 -  Differential Geometry  
Credits: 3  

An introduction to differential geometry in a classical setting: the study of n-surfaces, embedded in Euclidean space.

Prerequisites: MA 200, MA 202, and MA 215.   
Note(s): MA 270 recommended. Offered on sufficient demand.  
MA 313 -  Introduction to Topology  
Credits: 3  

Selected topics in topology such as metric spaces, point set topology of Euclidean spaces, introduction to algebraic topology.

Prerequisites: MA 113 and MA 215.   
Note(s): Normally offered spring semester of odd-numbered years.  
MA 316 -  Numerical Algorithms  
Credits: 3  

An introduction to using computation to obtain approximate solutions to mathematical problems. A variety of algorithms are studied, as are the limitations of using computational methods. Topics include algorithms for solving equations, systems, and differential equations; approximating functions and integrals; curve fitting; round-off errors, and convergence of algorithms.

Prerequisites: MA 111 (or both MA 108 and MA 109), CS 106, and MA 200.   
Note(s): Normally offered fall semester of even-numbered years.  
MA 319 -  Abstract Algebra I  
Credits: 4  

Survey of algebraic structures; groups, rings, fields, vector spaces, and linear transformations.

Prerequisites: MA 200 and MA 215.   
Note(s): Offered every semester.  
MA 320 -  Abstract Algebra II  
Credits: 3  

Selected topics in advanced algebra.

Prerequisites: MA 319.   
Note(s): Normally offered spring semester of even-numbered years.  
MA 323 -  Real Analysis  
Credits: 3  

Selected topics in real analysis.

Prerequisites: MA 303.   
Note(s): Offered on sufficient demand.  
MA 324 -  Complex Analysis  
Credits: 3  

Analytic functions, complex integration, complex sequences and series, and conformal mapping.

Prerequisites: MA 303.   
Note(s): Normally offered spring semester of even-numbered years.  
MA 325 -  Problem Solving In Mathematics  
Credits: 1  

Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

Prerequisites: QR2.   
Note(s): During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. May be repeated for credit. Must be taken S/U.  
MA 325H -  Honors: Problem Solving In Mathematics (Jr/Sr)  
Credits: 1  

Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 326H -  Honors: Problem Solving  
Credits: 1  

Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.

MA 331 -  Dynamical Systems  
Credits: 3  

A study of dynamical systems and their application. Topics covered include first-order equations, bifurcation theory, linear systems, phase plane analysis, and chaos. Examples will be considered from problems in medicine and the natural and social science.

Prerequisites: MA 270.   
Note(s): Normally offered fall semester of odd-numbered years.  
MA 351A-D -  Selected Topics in Mathematics  
Credits: 1-4  

Topics that complement the established upper level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.

Prerequisites: MA 215.  
MA 371A-D -  Independent Study Math  
Credits: 1-4  

Special study in mathematics outside the regular department offerings.

MA 376 -  Senior Seminar in Mathematics  
Credits: 3  

Research, discussion, and presentation of selected topics at an advanced level, to provide a capstone experience for the mathematics major; primarily intended for seniors. Senior Seminar in Mathematics - Research, discussion, and presentation of selected topics at an advanced level, to provide a capstone experience for the mathematics major; primarily intended for seniors.

Prerequisites: Senior status, MA 215, one 300-level course in Mathematics, in addition to any specific courses required by the instructor.   
Note(s): Offered spring semester. In exceptional circumstances non-senior students may be permitted to enroll in the course with department approval. This course may be repeated for credit with permission of the department. Fulfills Senior Experience Coda requirement.  
MA 381 -  Senior Thesis  
Credits: 3  

Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors.

Prerequisites: Permission of department.   
Note(s): Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors.  
MA 382 -  Senior Thesis  
Credits: 3  

Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors.

Prerequisites: Permission of department.  
MA 399A-D -  Internship in Mathematics  
Credits: 1-4  

Professional experience at an advanced level for juniors and seniors with substantial academic experience in mathematics. With faculty sponsorship and departmental approval, students may extend their educational experience in pure or applied mathematics. This course may not be used to satisfy the requirements of any major or minor in the department.

Prerequisites: MA 200, two additional courses in mathematics at the 200 level or above, and permission of department.   
Note(s): Not for liberal arts credit.