### Lauren Thorne/Roote

**Class of 2013**

I currently work at Scranton Preparatory School as an algebra and geometry teacher. My college math courses made me aware of the bigger picture in mathematics. They helped me to not only grasp each individual subject on a higher level, but also to understand their connection to one another so I can convey their practical relationships and importance in the greater field of mathematics to my high school students.

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## Mathematics Courses

### MATH 095 Fundamentals of Mathematics (3)

Topics include exponents, radicals, factoring, linear and quadratic equations, graphing of linear and polynomial functions, area, volume, systems of equations, and problem solving. **This course does not satisfy the core math requirements**.

### MATH 120 Mathematics in the Liberal Arts (3)

Designed to implement NCTM curriculum standards with emphasis on problem-solving, patterns and relationships, functions, estimation, and mathematical connections to other disciplines. Topics are chosen from this list: functions, mathematical modeling, basic trigonometry, geometry, astronomy, music, elementary statistics, voting methods, and logic. No prior knowledge of any of these topics is assumed. **There are no prerequisites for MATH 120 - Math Placement exams are not required for this course**.

### MATH 130 Mathematics for Contemporary Society (3) (Formerly MATH 110)

The topics studied will include techniques and applications of set theory, counting techniques, matrices, linear systems, statistics and probability, and linear programming. Prerequisite: passing grade in the Algebra Placement exam.

### MATH 150 Architectural Mathematics (3)

The principles of mathematics relating to architecture and building design. Topics include plane and solid geometry, coordinate systems, vectors, isometrics, the golden ratio, conic sections, tilings, fractals, and concepts in topology. Prerequisite: passing grade in the Algebra Placement exam.

### MATH 155 Statistics for the Behavioral and Social Sciences (3) (Formerly MATH 216)

Surveys the basic statistical concepts applicable to problems in the behavioral and social sciences. Includes descriptive statistics, regression and correlative, hypothesis testing, nonparametric methods, and analysis of variance. Computer software will be utilized for calculations. Prerequisite: passing grade in the Algebra Placement exam.

### MATH 160 Analysis of Functions (Pre-calculus) (3) (Formerly MATH 115)

Topics include polynomial, rational, exponential, logarithmic and trigonometric functions, as well as conic sections. Prerequisite: passing grade in the Algebra Placement exam.

### MATH 170 Applications of Mathematics to Biology (3)

Examines problems in biology through the use of a variety of mathematical tools and models. Topics are chosen from linear, exponential, and logarithmic functions, set theory, linear systems, probability, and an introduction to calculus. Prerequisites: algebra and trigonometry. Prerequisite: C or better in MATH 160, or passing the Calculus placement exam.

### MATH 201 Calculus with Analytic Geometry I (3)

Limits, continuity, differentiation, and applications, including related rates and extremum. Prerequisites: algebra and trigonometry. Prerequisite: C or better in MATH 160, or passing the Calculus placement exam.

### MATH 202 Calculus with Analytic Geometry II (3)

Integration, applications of the definite integral, logarithmic, exponential, hyperbolic, inverse hyperbolic, and trigonometric functions. Prerequisite: MATH 201.

### MATH 203 Calculus with Analytic Geometry III (3)

Improper integrals, indeterminate forms, infinite series, polar coordinates, parametric equations, and three-dimensional space. Prerequisite: MATH 202.

### MATH 204 Calculus with Analytic Geometry IV (3)

Vector-valued functions, partial derivatives, multiple integrals, and vector calculus. Prerequisite: MATH 203.

### MATH 219 History of Mathematics (3)

The study of mathematical concepts from arithmetic to calculus in their historical perspective. This study will be supplemented by historical background material, biographies of mathematicians and translations of source manuscripts in which mathematical discoveries were first announced. Attention will be given to the relationship of mathematics to other disciplines. For Mathematics majors and minors.

### MATH 220 Introduction to Probability and Statistics (3)

Acquaints the student with elements of probability, Bayes theorem, measures of central tendency, dispersion, probability distribution, hypothesis tests, nonparametric tests, linear regression, and correlation.

### MATH 271 Transition to Advanced Mathematics (3)

A transition from lower level mathematics courses to higher level courses. Emphasis will be placed on correct reading, understanding, and writing of proofs. Topics will include logic, direct proofs, proof by contra-positive, proof by contradiction, equivalence relations, functions, and mathematical induction.

### MATH 311 Differential Equations (3)

The study of differential equations and first-order linear systems through a combination of analytical, numerical, and qualitative techniques. Topics include the standard analytical methods of solving nth-order linear equations, eigenvalues and eigenvectors for systems, phase-plane trajectories, the Laplace transform, and numerical approximations. Technology is used in conjunction with theory to approximate and analyze solutions. Modeling physical phenomena is emphasized through a rich variety of applications. Prerequisite: MATH 204, MATH 271.

### MATH 321 Abstract Algebra (3)

Provides an introduction to groups, rings, ideals, integral domains and fields. Prerequisite: MATH 202, MATH 271.

### MATH 322 Linear Algebra (2)

Deals with vector spaces, matrices, linear transformations, canonical forms and determinants. Must be taken with MATH 322L. Prerequisite: MATH 202, MATH 271.

### MATH 322L Linear Algebra Lab (1)

Laboratory to accompany MATH 322 in order to use a computer algebra system (such as Mathematica or Maple) to provide visual re-enforcement of central concepts. Must be taken with MATH 322.

### MATH 323 Theory of Numbers (3)

An introduction to basic number theory: properties of the integers, congruence, Fermat's and Wilson's Theorem, number theoretic functions, Diophantine equations and primes. Prerequisite: MATH 202, MATH 271.

### MATH 324 College Geometry (3)

The study of axiomatic systems and the notions of proof and consistency. Examines finite, elliptical, and hyperbolic geometries, and advanced topics in Euclidean Geometry. Software is used to enhance exploration and discovery of theorems. Prerequisite: MATH 202, MATH 271.

### MATH 411B Curriculum Methods and Materials in Mathematics (3)

See EDUC 411.

### MATH 420 Discrete Mathematics (3)

An introduction to the algebraic concepts, methods and techniques that form the theoretical basis for computer science, including relevant areas of logic, set theory, relations and functions, and Boolean algebra. Prerequisite: MATH 202, MATH 271.

### MATH 425 Topology (3)

Introduction to point-set topology at the undergraduate level. Topics include topological spaces, limit points, continuity, connectedness, compactness, separability, and the fundamental group. Prerequisite: MATH 204, MATH 271.

### MATH 430 Real Analysis (3)

An introduction to the analysis of real numbers, variables, and functions. Topics include topology of the real numbers, sequences and series, limits, continuity and uniform continuity, differentiation, the Riemann integral, and sequences of functions. Prerequisite: MATH 204, MATH 271.

### MATH 440 Complex Variables (3)

An introduction to the theory of complex numbers, variables, and functions. Topics include transformations and mappings, elementary and analytic functions, complex integration and Cauchy’s theorem, Taylor and Laurent expansions, residues, harmonic functions, and conformal mappings. Prerequisite: MATH 204, MATH 271.

### MATH 447 Special Projects (variable credit)

Definition, formulation, solution, documentation, and testing of a problem under close faculty supervision.

### MATH 456 Mathematical Statistics (3)

Deals with probability distributions, limit theorems, estimation, hypothesis tests, correlation and regression, analysis of variance. Prerequisites: MATH 204, 220.

### MATH 495 Senior Seminar (1)

Analysis of the underlying foundational questions of mathematics including the notions of proof and consistency within a specific mathematical framework. Examination of the considerable impact of mathematics on culture and society from ancient to modern times.

### MATH 498 Special Topics (variable credit)

Special topics in mathematics.