# Mathematics

**Program Overview**

Students majoring in mathematics at Rider are met with rigorous and insightful instruction. Courses progress from foundational topics to advanced theories and techniques. Faculty members are active in research and will invite, stimulate and support students' curiosity and understanding.

Graduates of Rider’s mathematics program go on to careers in such fields as education, scientific and medical research, engineering, computer science, architecture, pharmaceutical research, actuarial science, and urban planning and development.

**Curriculum Overview**

Requirements for the math major total 50 semester hours and include calculus I, II and III, linear algebra, differential equations, advanced calculus, modern geometry, probability and statistical analysis I, modern algebra, complex analysis and mathematics electives. Also required are general physics I and II.

## Honors Program in Mathematics

Superior students majoring in mathematics may participate in a program leading to graduation with honors in mathematics. A candidate must submit a written application by March 1 of the junior year to the departmental honors committee. Admission to the program will be based on a 3.25 cumulative average in mathematics courses taken in the first five semesters and sponsorship by a member of the departmental faculty. During the senior year, the student will be enrolled in MTH 490 Independent Research and Study. Honors in mathematics is based on earning a 3.4 average in seven mathematics courses at the 300 and 400 levels (excluding MTH 490) and an acceptable senior thesis. Further information on the program can be obtained from the department.

**Degrees Offered**

- B.A. in Mathematics

**Contact**

**James Ottavio Castagnera, J.D., Ph.D.**

Acting Chairman

Moore Library 120

609-896-5035

castagne@rider.edu

**Program Website:** Mathematics

**Associated Department/College:** Department of Mathematics

**Related Programs**

## Requirements for the Major

(50 credits)

Code | Title | Credits |
---|---|---|

2017 General Education Requirements | 45-46 | |

MTH 210 & MTH 211 & MTH 212 | Calculus I and Calculus II and Calculus III | 12 |

MTH 240 | Linear Algebra | 3 |

MTH 250 | Differential Equations | 3 |

MTH 308 | Advanced Calculus | 3 |

MTH 315 | Modern Geometry | 3 |

MTH 340 | Probability & Stat Analysis I | 3 |

MTH 401 | Modern Algebra | 3 |

MTH 410 | Complex Analysis | 3 |

Three 400-level mathematics electives (excluding MTH 490) or one 300-level and two 400-level mathematics electives (excluding MTH 490) | 9 | |

Physics | ||

PHY 200 | General Physics I | 4 |

PHY 201 | General Physics II | 4 |

Total Credits | 95-96 |

Mathematics majors must attain a “B” average in Calculus I and II in order to take advanced mathematics courses.

## Requirements for the Minor

(24 credits)

Code | Title | Credits |
---|---|---|

MTH 210 & MTH 211 & MTH 212 | Calculus I and Calculus II and Calculus III | 12 |

Four mathematics courses above the MTH 212 level | 12 | |

Total Credits | 24 |

The following educational plan is provided as a sample only. Rider students who do not declare a major during their freshman year, who change their major, or those who transfer to Rider will follow a different plan to ensure a timely graduation. Each student, with guidance from his or her academic advisor, will develop a personalized educational plan.

Year 1 | ||
---|---|---|

Fall Semester | Credits | |

CMP 120 | Expository Writing ^{1} | 3 |

MTH 210 | Calculus I | 4 |

HIS 150 | World History to 1500 | 3 |

Social Science Core (1 of 2) | 3 | |

Level 1 Foregin Language Core | 3 | |

NCT 010 | Freshman Seminar | 0 |

Semester Credit Hours | 16 | |

Spring Semester | ||

CMP 125 | Research Writing | 3 |

MTH 211 | Calculus II | 4 |

HIS 151 | World History Since 1500 | 3 |

Level 2 Foreign Language Core | 3 | |

Semester Credit Hours | 13 | |

Year 2 | ||

Fall Semester | ||

MTH 212 | Calculus III | 4 |

MTH 240 | Linear Algebra | 3 |

PHY 200 & 200L | General Physics I and General Physics I Lab | 4 |

Social Science Core (2 of 2) | 3 | |

Fine Arts Core | 3 | |

Semester Credit Hours | 17 | |

Spring Semester | ||

MTH 250 | Differential Equations | 3 |

MTH 315 | Modern Geometry | 3 |

PHY 201 & 201L | General Physics II and General Physics II Lab | 4 |

Literature Core | 3 | |

Elective Course Credits ^{2} | 3 | |

Semester Credit Hours | 16 | |

Year 3 | ||

Fall Semester | ||

MTH 308 | Advanced Calculus | 3 |

MTH 340 | Probability & Stat Analysis I | 3 |

Philosophy Core (Any Philosophy course or AMS 227) | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Semester Credit Hours | 15 | |

Spring Semester | ||

MTH 410 | Complex Analysis | 3 |

Math Elective | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Semester Credit Hours | 15 | |

Year 4 | ||

Fall Semester | ||

MTH 401 | Modern Algebra | 3 |

Math Elective | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Semester Credit Hours | 15 | |

Spring Semester | ||

Math Elective | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Elective Course Credits ^{2} | 3 | |

Semester Credit Hours | 15 | |

Total Credits | 122 |

^{1} | For course placement information please visit this website. |

^{2} | Please note that elective credits may be used to complete requirements in a second major or minor. |

**MTH 100S Math Skills Lab 1 Credits**

The Math Skills Lab helps science majors master arithmetic and elementary algebra necessary for college level mathematics courses. Entering science majors with SAT math scores below 570 must take this course before MTH 105. Students are required to attend regular class sessions. Students have access to tutors, computer-assisted instruction, and structured workshops. The one supplemental education unit does not count toward graduation; grading is done on a Y/Z (pass/not pass) basis.

**MTH 102 Finite Mathematics 3 Credits**

The course begins with consolidation of some basic topics including sets, number theory, real numbers, functions, and graphs. Statistics and probability theory are introduced with applications to the social and natural sciences. Throughout the course there will be an emphasis on formulating and solving familiar sorts of problems in mathematical terms.

**MTH 105 Algebra and Trigonometry 4 Credits**

Algebraic functions, trigonometric functions, identities and conditional equations, inequalities, exponential and logarithmic functions. Prerequisite(s): A mathematics SAT score of 570 or ACT score of 26, or a mathematics SAT score of 550 or ACT score of 23 plus a passing score on the Algebra section of the math and science majors placement test.

**MTH 120 Introduction to Applied Statistics 3 Credits**

Collection and presentation of data. Measures of location and variation, sampling theory, hypothesis testing, confidence intervals, t-tests, chi-square tests, regression, and correlation. Emphasizes practical applications. Not open to business administration, chemistry, environmental, geosciences, marine sciences, math or liberal studies: marine ecological or environmental emphasis majors.

**MTH 150 Mathematics for Education Majors I 3 Credits**

This is the first course in a three-course sequence for elementary education majors, This course covers the concept of Numbers, starting with counting numbers, decimals, negative numbers, fractions, and real numbers; different ways of representing numbers, and the relations between them are explored; different meanings and applications of the arithmetic operations are studied; standard and non-standard algorithms for arithmetic are considered in light of the representation of numbers. May not be used by SLAS students to satisfy the mathematics component of the core
Prerequisite(s): A mathematics SAT score of 550 or ACT score of 23; A passing score on the Math Skills placement Test; or passing MTH 100S with grade of Y.
.

**MTH 151 Mathematics for Education Majors II 3 Credits**

This is the second course in a three-course sequence for elementary education majors. In this course, students will study proportional reasoning, Number Theory, Algebra, Geometry, and measurement. May not be used by SLAS students to satisfy the mathematics component of the core.

**Prerequisite**(s): MTH 150.

**MTH 152 Mathematics for Education Majors III 3 Credits**

This is the third course in a three-course sequence for elementary education majors. In this course, students will study area and volume, transformational geometry, statistics and probability.

**Prerequisite**(s): MTH 151.

**MTH 210 Calculus I 4 Credits**

Introduces analytic geometry, functions, limits, and derivatives; differentiation of algebraic and trigonometric functions, curve sketching, maxima and minima, and higher derivatives. Prerequisite(s): A mathematics SAT score of 670 or ACT score of 29 ; or a mathematics SAT score of 570 or ACT score of 23 and a passing score on the Pre-Calculus Section of the Math and Science Majors Placement test; or passing MTH 105.

**Prerequisite**(s): MTH 105.

**MTH 211 Calculus II 4 Credits**

The definite integral, differentiation of transcendental functions, methods of integration and approximate integration, determination of area, volume, and surface area.

**Prerequisite**(s): MTH 210.

**MTH 212 Calculus III 4 Credits**

Infinite series; functions of two and three variables, vectors and tangent planes, partial derivatives, multiple integrals, determination of volume and density.

**Prerequisite**(s): MTH 211.

**MTH 230 Discrete Mathematics 4 Credits**

An introduction to topics in Discrete Mathematics. This course covers methods of proof, induction and recursion, and other topics in discrete mathematics. Topics may include graph theory, trees, and symmetry groups.

**MTH 240 Linear Algebra 3 Credits**

Systems of linear equations; vector spaces; linear independence; determinants; orthogonality; linear maps; eigenvectors.

**Prerequisite**(s): MTH 210 or as corequisite; sophomore standing; or permission of instructor.

**MTH 250 Differential Equations 3 Credits**

First order differential equations, separable and exact; integrating factors; second order linear differential equations; series solutions of second order linear differential equations; higher order equations; existence and uniqueness theorems; systems of linear differential equations. Prerequisite(s): MTH 240, MTH 211.

**Corequisite**(s): MTH 212 or as prerequisite.

**MTH 308 Advanced Calculus 3 Credits**

Vectors, gradients, and directional derivatives, Lagrange multipliers, Taylor’s theorem, multiple integrals, change of variables, line and surface integrals, Stokes’ theorem.

**Prerequisite**(s): “B” average in MTH 210 and MTH 211; MTH 212, MTH 240.

**MTH 315 Modern Geometry 3 Credits**

Covers geometry from a modern point of view, with emphasis on non-Euclidean geometry, particularly projective geometry.

**MTH 340 Probability & Statistical Analysis I 3 Credits**

Theory of sets and probability; discrete and continuous random variables and probability distributions. Emphasizes foundations and utilizes the techniques of the calculus.

**MTH 341 Probability & Statistical Analysis II 3 Credits**

Continuation of MTH 340. Foundations of mathematical statistics: normal distributions, estimation, confidence intervals and hypothesis testing; topics chosen from student’s t- test, chi-square tests, analysis of variance and regression analysis. Emphasizes foundations and utilizes the techniques of the calculus.

**Prerequisite:** MTH 340. Spring.

**MTH 401 Modern Algebra 3 Credits**

Provides an introduction to modern abstract algebra. It emphasizes the axiomatic method to analyze the major algebraic systems. The instructor will choose the topics to be studied from among the following algebraic structures: integral domains, fields, complete ordered fields, groups, polynomials, rings, ideals and modules.

**Prerequisite**(s): MTH 240.

**MTH 402 Topics in Advanced Mathematics 3 Credits**

Chosen from advanced pure or applied mathematics. Topics vary, depending on instructor.

**Prerequisite**(s): MTH 308.

**MTH 410 Complex Analysis 3 Credits**

Analytic functions, conformal mapping, power series, Cauchy’s theorem, calculus of residues.

**Prerequisite**(s): MTH 308.

**MTH 420 Number Theory 3 Credits**

Covers topics including divisibility theory, the prime numbers, the theories of congruences and of quadratic reciprocity, and Fermat’s Last Theorem. Other topics may also include applications to cryptography, Pell’s equations, continued fractions, and the theory of partitions.

**Prerequisite**(s): MTH 240 or permission of instructor.

**MTH 430 Introduction to Topology 3 Credits**

A comprehensive introduction to elementary topology. The concepts of topological spaces and metric spaces will be introduced. Connectedness, compactness and properties of subsets of the real numbers rooted in topology will also be considered. The quotient topology will be used to construct surfaces as identification spaces, and tools will be developed to distinguish one surface from another.

**Prerequisite**(s): MTH 212.

**MTH 440 Real Analysis 3 Credits**

Covers the theory of sets, the real number system and its properties, convergence of sequences and series of numbers and functions, and the theory of integration, including: measure theory, the Riemann integral, and introduction to the Lebesque theory of integration.

**Prerequisite**(s): MTH 308 or as corequisite.

**MTH 490 Independent Research and Study 1-4 Credits**

Immerses the student in research and mathematical literature. If possible, the student will publish the results or present them at a scientific meeting.