Mathematics and Statistics
Department Overview
Mathematics is an academic discipline which is fascinating to study in its own right but also has very wide-ranging applications throughout the modern world. Our faculty are all skilled and dedicated teachers as well as active scholars; we strive to make each course we offer engaging and challenging. Our graduates go on to a great variety of careers in such areas as theoretical mathematics, actuarial science, applied mathematics, teaching at various levels, and many more.
Advice for Students Beginning the Study of College Mathematics
Students who plan to study mathematics at Skidmore should take the online Calculus Placement Exam prior to the beginning of classes (www.skidmore.edu/mcs/calcplacement.php). Based on the results of this exam, the department will recommend in which courses of the sequence the student should begin:
Code | Title | Hours |
---|---|---|
MA 108 & MA 109 | Calculus with Algebra I and Calculus with Algebra II (a two-semester version of Calculus I for students who need additional pre-calculus preparation) | 6 |
MA 111 | Calculus I | 4 |
MA 113 | Calculus II | 4 |
MA 200 | Linear Algebra | 4 |
MA 211 | Calculus III | 3 |
Credit for Advanced Placement
Students receiving a score of 4 or 5 on the Math AB AP exam will receive credit for having taken MA 111 Calculus I. Students receiving a score of 4 or 5 on the Math BC AP exam will receive credit for having taken MA 113 Calculus II. Students receiving a score of 4 or 5 on the Statistics AP exam will receive credit for having taken MS 104 Introduction to Statistics.
Chair of the Department of Mathematics and Statistics: Julie Douglas
Associate Chair: Lucy Oremland
QR Coordinator: Csilla Szabo
S3M Program Director: Rebecca Trousil
Professors: Julie Douglas, Mark Hofmann; R. Daniel Hurwitz; Mark E. Huibregtse, Rachel Roe-Dale, The Class of 1964 Term Professorship; David C. Vella
Assistant Professors: Kirsten Hogenson, Vojtech Kejzlar, Lucy Oremland
Visiting Assistant Professors: Cristobal Lemus-Vidales
Teaching Professors: Csilla Szabo, Rebecca Trousil
Lecturers: Megan DiMaio, ^{1}Bert Rawert, ^{1}Rachel Seligman
- ^{ 1 }
Part-time
Mathematics B.A.
For Students Who Entered Skidmore in Fall 2019 and Beyond
Students majoring in mathematics fulfill the departmental requirements by completing 10 courses. Nine of the courses must be in mathematics or a designated course in statistics at the 200 level or above, to include:
Code | Title | Hours |
---|---|---|
Required Courses ^{1, 5} | ||
MA 200 | Linear Algebra | 4 |
MA 211 | Calculus III | 3 |
MA 213 | Calculus IV | 3 |
MA 215 | Introduction to Mathematical Reasoning and Proof ^{2} | 4 |
MA 303 | Introduction to Analysis | 4 |
MA 319 | Abstract Algebra I | 4 |
MA 376 | Senior Seminar in Mathematics | 3 |
Select two additional courses, at least one of which is at the 300 level ^{3,4} | 6-8 | |
CS 106 | Introduction to Computer Science I | 4 |
or CS 206 | Introduction to Computer Science II | |
Total Hours | 35-37 |
- ^{ 1 }
No more than 4 credit hours of S/U can be used toward the major. (**For students who entered Skidmore in Fall 2021 and beyond: The following courses are excluded: MA 215 Introduction to Mathematical Reasoning and Proof, MA 303 Introduction to Analysis, MA 319 Abstract Algebra I, MA 376 Senior Seminar in Mathematics, MA 381 Senior Thesis, MA 382 Senior Thesis.)
- ^{ 2 }
In MA 215 Introduction to Mathematical Reasoning and Proof, students will acquire writing skills that are necessary to work on advanced material in mathematics and will fulfill the writing requirement in the major.
- ^{ 3 }
Either MS 204 Statistical Methods or MS 240 Applied Regression Analysis can count towards the mathematics major
- ^{ 4 }
- ^{ 5 }
For students who entered Skidmore in Fall 2021 and beyond MS-204 is required for the mathematics major.
Students interested in pursuing graduate work in (theoretical) mathematics should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 313 | Introduction to Topology | 3 |
MA 320 | Abstract Algebra II | 3 |
MA 324 | Complex Analysis | 3 |
MA 302 | Graph Theory | 3 |
Students interested in applied mathematics should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 270 | Differential Equations | 4 |
MA 331 | Dynamical Systems | 3 |
MA 324 | Complex Analysis | 3 |
MA 316 | Numerical Algorithms | 3 |
Students interested in mathematics education should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 214 | Theory of Numbers | 3 |
MA 309 | Elements of Modern Geometry | 3 |
MA 310 | History of Mathematics | 3 |
MS 204 | Statistical Methods | 4 |
For Students Who Entered Skidmore Prior to Fall 2019
Students majoring in mathematics fulfill the departmental requirements by completing nine courses. Eight of the courses must be in mathematics or a designated course in statistics at the 200 level or above, to include:
Code | Title | Hours |
---|---|---|
Required Courses ^{1, 5} | ||
MA 200 | Linear Algebra | 4 |
MA 202 | Calculus III ^{2} | 4 |
MA 215 | Introduction to Mathematical Reasoning and Proof ^{3} | 4 |
MA 303 | Introduction to Analysis | 4 |
MA 319 | Abstract Algebra I | 4 |
MA 376 | Senior Seminar in Mathematics | 3 |
Select two additional courses, at least one of which is at the 300 level ^{4} | 6-8 | |
CS 106 | Introduction to Computer Science I | 4 |
or CS 206 | Introduction to Computer Science II | |
Total Hours | 33-35 |
- ^{ 1 }
No more than 8 credit hours of S/U can be used toward the major.
- ^{ 2 }
Because MA 202 Calculus III will no longer be offered after spring 2019, students will need to fulfill this major requirement by taking MA 211 Calculus III and MA 213 Calculus IV or by fulfilling MA 202 Calculus III with transfer credit.
- ^{ 3 }
In MA 215 Introduction to Mathematical Reasoning and Proof, students will acquire writing skills that are necessary to work on advanced material in mathematics and will fulfill the writing requirement in the major.
- ^{ 4 }
- ^{ 5 }
For students who entered Skidmore in Fall 2021 and beyond MS-204 is required for the mathematics major.
Students interested in pursuing graduate work in (theoretical) mathematics should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 313 | Introduction to Topology | 3 |
MA 320 | Abstract Algebra II | 3 |
MA 324 | Complex Analysis | 3 |
MA 302 | Graph Theory | 3 |
Students interested in applied mathematics should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 270 | Differential Equations | 4 |
MA 331 | Dynamical Systems | 3 |
MA 324 | Complex Analysis | 3 |
MA 316 | Numerical Algorithms | 3 |
Students interested in mathematics education should include as many of the following courses as possible in their programs:
Code | Title | Hours |
---|---|---|
MA 214 | Theory of Numbers | 3 |
MA 309 | Elements of Modern Geometry | 3 |
MA 310 | History of Mathematics | 3 |
MS 204 | Statistical Methods | 4 |
Mathematics Minor
Students minoring in mathematics fulfill the departmental requirements by completing:
Code | Title | Hours |
---|---|---|
Required Courses ^{1,2} | ||
MA 113 | Calculus II | 4 |
MA 200 | Linear Algebra (or the equivalent) | 4 |
MA 215 | Introduction to Mathematical Reasoning and Proof | 4 |
MA 303 | Introduction to Analysis | 4 |
or MA 319 | Abstract Algebra I | |
Select two more 3- or 4-credit courses in mathematics at the 200 or 300 level ^{3} | 6-8 | |
Total Hours | 22-24 |
- ^{ 1 }
No more than 8 credit hours of S/U may be used toward the minor.
- ^{ 2 }
For students entering Skidmore in Fall 2021 and beyond: No more than 4 credit hours of S/U may be used toward the minor. The following courses must be taken for a letter grade: MA 215 Introduction to Mathematical Reasoning and Proof, MA 303 Introduction to Analysis, MA 319 Abstract Algebra I, MA 376 Senior Seminar in Mathematics, MA 381 Senior Thesis, MA 382 Senior Thesis.
- ^{ 3 }
Additionally, either MS 204 Statistical Methods or MS 240 Applied Regression Analysis can count towards the mathematics minor.
Statistics Minor
Effective for Those Who Entered Skidmore in Fall 2018 and Beyond
The minor in statistics requires completing five 3- or 4-credit courses. These must include two core courses and three elective courses from the list below. Three of the five courses must be designated MA or MS.
Code | Title | Hours |
---|---|---|
Required Courses ^{1} | ||
Introductory Statistics Core Course | ||
Select one of the following: | 4 | |
Introduction to Statistics ^{2} | ||
Statistical Methods (strongly recommended) ^{2} | ||
Biostatistics | ||
Statistical Methods | ||
Statistics and Research Methods I | ||
Statistics Core Course | ||
MS 240 | Applied Regression Analysis | 4 |
Elective Courses ^{3,4,5} | ||
Select three of the following: | 9-12 | |
Courses in Statistics and Mathematics: | ||
Data Visualization | ||
MS 251C | ||
MS 251C | ||
MA 351C & MA 351D | and | |
Approved Outside Elective Courses: | ||
Applied Data Science | ||
Advanced Topics in Computer Science | ||
Applied Econometrics | ||
Advanced Topics In Economics | ||
Data Analysis, Modeling, and Scientific Programming: Earth and Environmental Sciences | ||
Introduction to GIS | ||
ID 351 | ^{6} | |
Experiments in Political Science | ||
Research Methods 2: Intermediate Statistics | ||
PS 327 | ||
Social Research Methods | ||
Total Hours | 17-20 |
- ^{ 1 }
No more than 4 credit hours of S/U may be used toward the minor.
- ^{ 2 }
Students who have taken MS 104 Introduction to Statistics are not eligible to take MS 204 Statistical Methods (and vice versa).
- ^{ 3 }
The senior seminar (MA 376 Senior Seminar in Mathematics) may count as an elective toward the minor if the topic is statistical and with the approval of the department.
- ^{ 4 }
An independent study or honors project that involves substantial statistical analysis may count toward the minor with the consent of the department.
- ^{ 5 }
Other elective courses from outside the department that include a substantial statistical component may count toward the minor with the consent of the department.
- ^{ 6 }
And its previous versionID 351C Advanced Spatial Analysis
Effective for Those Who Entered Skidmore Prior to Fall 2018
The minor in statistics requires completing five 3- or 4-credit courses. These must include one core course and four elective courses from the list below.
Code | Title | Hours |
---|---|---|
Required Courses ^{1} | ||
Introductory Statistics Core Course | ||
Select one of the following: | 4 | |
Introduction to Statistics ^{2} | ||
Statistical Methods (strongly recommended) ^{2} | ||
Biostatistics | ||
Statistical Methods | ||
Statistics and Research Methods I | ||
Elective Courses ^{3,4,5} | ||
Select four of the following: ^{6} | 12-16 | |
Courses in Statistics and Mathematics: | ||
Data Visualization | ||
Applied Regression Analysis | ||
MS 251C | ||
MA 351C | ||
Approved Outside Elective Courses: | ||
Advanced Topics in Computer Science | ||
Applied Econometrics | ||
Advanced Topics In Economics | ||
Data Analysis, Modeling, and Scientific Programming: Earth and Environmental Sciences | ||
Experiments in Political Science | ||
Research Methods 2: Intermediate Statistics | ||
PS 327 | ||
Social Research Methods | ||
Total Hours | 16-20 |
- ^{ 1 }
No more than 4 credit hours of S/U may be used toward the minor.
- ^{ 2 }
Students who have taken MS 104 Introduction to Statistics are not eligible to take MS 204 Statistical Methods (and vice versa).
- ^{ 3 }
The senior seminar (MA 376 Senior Seminar in Mathematics) may count as an elective toward the minor if the topic is statistical and with the approval of the department.
- ^{ 4 }
An independent study or honors project that involves substantial statistical analysis may count toward the minor with the consent of the department.
- ^{ 5 }
Other elective courses from outside the department that include a substantial statistical component may count toward the minor with the consent of the department.
- ^{ 6 }
At least two must be designated MA or MS
Honors
For Students Graduating in May 2021 and Beyond
Students wishing to qualify for departmental honors in the mathematics major must:
Portfolio Option
- complete all departmental requirements for the mathematics major and have a GPA of 3.75 or higher for all course work (MA, MS) taken in the department;
- have a GPA of 3.0 for all course work taken at Skidmore;
- file with the Department a declaration of intention to qualify for honors by the end of the official add-drop period during the semester of graduation; and
- Submit a portfolio which demonstrates the student’s commitment to the field of mathematical sciences and contributions to the Department. Portfolios will be read by the review committee to see if the work is of the exceptional quality that merits honors. The review committee will submit its recommendation to the Department for final adjudication.
Or Thesis Option
- complete all departmental requirements for the mathematics major and have a GPA of 3.50 or higher for all course work (MA, MS) taken in the department;
- have a GPA of 3.0 for all course work taken at Skidmore;
- file with the Department a declaration of intention to qualify for honors by the end of the official add-drop period during the semester of graduation; and
- submit an honors thesis to be read by a review committee, and give an oral presentation of the thesis to the department. The review committee will evaluate the thesis to determine if it is of the exceptional quality that merits honors; the committee’s recommendation will be submitted to the department for final adjudication.
Pi Mu Epsilon, New York Alpha Theta Chapter
Incorporated in 1914, Pi Mu Epsilon is a national honorary society whose purpose is the promotion of scholarly activity in mathematics. Undergraduate students are qualified for membership if they meet one of the following criteria:
- upperclassmen who have completed at least two years of college mathematics, including calculus, with at least a B average and who are in the top third of their class in general college work;
- sophomores, majoring in or intending to major in mathematics, who have completed at least three semesters of college mathematics, including one year of calculus, with a straight-A record and who are in the top quarter of their class in general college work;
- senior mathematics majors may also qualify with a 3.0 or better overall GOA and a 3.5 or better GPA for all MA and MS courses at the 200 and 300 levels.
Course Listing
All MA and MC courses (except MA 100 Quantitative Reasoning) have the satisfaction of QR1 as a prerequisite.
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.
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.
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.
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.
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.
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.
Derivatives, integrals and their applications. Techniques of differentiation. Integration and differentiation of exponential, logarithmic and trigonometric functions.
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.
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.
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.
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.
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.
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.
Vector spaces, matrices and linear transformations, determinants, solution of linear equations.
Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, and line integrals.
Elementary probability, discrete and continuous random variables, theory of expectation, analysis of distribution functions.
Sequences and Series. Introduction to multivariable calculus. Taylor Series of a function. Topics include vector functions, partial derivatives, gradients.
Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, line integrals, surface integrals, vector calculus, divergence and curl.
Topics in classical and modern number theory including congruences, Diophantine equations, quadratic residues.
An introduction to mathematical proof and concepts of abstract mathematics, including elementary logic, methods of proof, set theory, functions and relations.
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.
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.
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.
Topics that complement the established lower level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.
An introduction to the theory and applications of differential equations.
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.
An introduction to the theory and applications of graphs. Topics may include graphs and digraphs, connectivity, trees, Euler and Hamiltonian cycles, and graph embeddings.
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.
Study of various topics in modern geometry, with emphasis on the axiomatic method.
Study of the development of mathematical ideas.
An introduction to differential geometry in a classical setting: the study of n-surfaces, embedded in Euclidean space.
Selected topics in topology such as metric spaces, point set topology of Euclidean spaces, introduction to algebraic topology.
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.
Survey of algebraic structures; groups, rings, fields, vector spaces, and linear transformations.
Selected topics in advanced algebra.
Selected topics in real analysis.
Analytic functions, complex integration, complex sequences and series, and conformal mapping.
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.
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.
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.
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.
Topics that complement the established upper level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.
Special study in mathematics outside the regular department offerings.
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.
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.
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.
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.
An introduction to fundamental concepts in statistical reasoning. Students will consider contexts, both historical and modern, in which statistical approaches arose and methodologies developed. Topics considered will include organization and analysis of data, the drawing of inferences from these data, and the careful presentation of these inferences. Examples will be drawn from a variety of disciplines.
An introduction to statistical methods. Students will learn sampling strategies, exploratory data analysis, hypothesis testing, and randomization-based strategies, with examples from a variety of disciplines. This course is designed for majors in STEM fields and/or those with strong quantitative skills.
An introduction to data visualization. Students will learn to use data visualization tools, to objectively critique and redesign graphics, and to produce and describe visualizations using the R/RStudio statistical software. A willingness to code is needed. (Fulfills QR2 requirement).
A continuation of introductory statistics, this course is intended for students in the physical, social, or behavioral sciences. Topics include multiple linear regression, indicator variables, model diagnostics, transformations and selection strategies, logistic and multiple logistic regression, and analysis of variance. Emphasis will be on applying tools to real data as well as the interpretation of results. The class will make extensive use of the R/RStudio statistical software, which is free to download and use.
Topics that complement the established lower level course offerings in statistics will be selected. Emphasis will be on the nature of statistical thought.
Exploration of a research topic in statistics. The students, in collaboration with a faculty mentor, will participate in a research project in a particular area of statistics which may be related to the faculty member’s research program.
Topics that complement the established upper-level course offerings in statistics.
Special study in statistics outside the regular department offerings.