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Mathematics B.A.

Students listening and engaging in class.

Mathematics, B.A.

Overview

B.A. Program

This program has fewer required courses in mathematics so students have more free credits to explore other disciplines or further expand their mathematical experience. This program is particularly suited for students who wish to combine mathematics with another major. The college has a strong history in education, and this degree would complement the education department, allowing students who wish to become secondary school teachers of mathematics to complete their master’s degree in education at D’Youville College. A total of 11 mathematics courses (36 hours) are required, consisting of 8 required courses (27 hours) and 3 electives (9 hours). In addition, two semesters of physics with lab (8 credit hours) are required – either PHY 101, 101L, 102, 102L or PHY 103, 103L, 104, 104L – these courses are in addition to the seven credits of core science.

Courses

Course Requirements

Mathematics
Degree: B.A.

Course Requirements for the Major:

Course Number Course Name Credits
*MAT 125

Calculus I

Basic theory of functions, limits, continuity, derivatives and integrals are taught. Some emphasis is placed on the structure of the real number system.

Prequisites: MAT-122 or have an SAT Math Sub-score 600+ or ACT 26+.

4
*MAT 126

Calculus II

The course explores the basic techniques for integration as well as elementary transcendental functions and the applications of differential and integral calculus.

Prequisites: MAT-125

4
MAT 202

Calculus III

The subject matter includes multivariate calculus, infinite series, differential equations and matrix algebra.
Offered in: Fall Only
Prequisites: MAT-126

4
MAT 300

Introduction to Mathematical Reasoning

This course introduces the student to abstract mathematics and proofs. Topics covered in the course include logic, sets, relations, functions, proofing methods (including proof by induction, contrapositive and contradiction) and cardinality.

Prequisites: MAT-126

3
MAT 301

Real Analysis I

The study of real-valued functions of one variable properties include continuity, uniform continuity and differentiation.
Offered in: Fall Only
Prequisites: Mat-202 Mat-300

3
MAT 315

Linear Algebra

An introduction to linear systems including matrices, determinants, linear transformations, vector spaces and linear independence. The student will perform most of the computation on a computer, so that familiarity with at least one higher-level programming language is presupposed. Applications include linear programming, graph theory, least squares, Markov chains and differential equations.

Prequisites: Mat-126 Mat-300, CSC-151 or IT-111

3
MAT 401

Abstract Algebra I

In this course, you will cover groups, quotient groups, homomorphisms, rings and fields.
Offered in: Fall Only
Prequisites: Mat-126 Mat-300

3
MAT 402

Abstract Algebra II

This course covers vector spaces, extension fields, elements of Galois theory.
Offered in: Spring Only
Prequisites: Mat-401

3

*Courses require a minimum grade of B-.
SUBTOTAL: 27

Mathematics Electives (select three of the following):

Course Number Course Name Credits
MAT 303

Foundations of Geometry I

This course is a study of symmetry and isometry in two- and three-dimensional space from both the Euclidean and Cartesian viewpoints. Inversion geometries will also be covered as well as group of transformations.

Prequisites: Mat-202 Mat-300

3
MAT 304

Foundations of Geometry II

This course covers affine, projective, absolute and hyperbolic geometries as well as vectors and differential geometries. Students will cover some topological problems. Prerequisite: MAT 303

Prequisites: MAT-303

3
MAT 310

Foundations of Mathematics

This course is a survey of the development of mathematical thought. Prerequisites: MAT 126 and MAT 300.

Prequisites: MAT-126 MAT-300

3
MAT 318

Discrete Math

Discrete mathematics includes topics that are particularly important in computer science. This course provides the student with an introduction to elementary combinatorics (counting methods and graph theory), elementary Boolean algebra and automata theory.

Prequisites: Mat-126

3
MAT 321

Differential Equations

This course will describe the classical methods for solving first order differential equations, systems of first order differential equations and equations of higher degree.

Prequisites: Mat-126 Mat-300

3
MAT 375

Math Modeling in Biology

Techniques for expressing biological molecules and concepts as mathematical expressions for analysis and comparison.

Prequisites: (BIO-102 BIO-102L) or (BIO-303 BIO-303L), MAT-125, 1 computer science (CSC or IT) course. CSC-151 orIT-111 prefered.

3
MAT 389

Special Topics

This course represents an opportunity to study a selected topic in mathematics. Topics originate with faculty or students.

Prequisites: None

3
MAT 402

Abstract Algebra II

This course covers vector spaces, extension fields, elements of Galois theory.
Offered in: Spring Only
Prequisites: Mat-401

3
MAT 403

Probability

This course is an introduction to probability and basic distribution theory, mathematical expectation, discrete and continuous functions, and generating function.

Prequisites: Mat-126 Mat-300

3
MAT 404

Mathematical Statistics

The theory of the mathematics of statistics; sampling distributions; point and interval estimation; theory and application of testing hypotheses, regression and correlation will all be covered in this course.

Prequisites: Mat-403

3
MAT 407

Senior Seminar I

This course provides an opportunity for dialogue between the senior mathematics major and faculty and peers on mathematical questions. A research paper of a theoretical nature is developed by the student and presented in the group. Prerequisites: Senior status in major or permission of the instructor; Offered as needed.

Prequisites: None

2
MAT 408

Senior Seminar II

This course provides an opportunity for dialogue between the senior mathematics major and faculty and peers on mathematical questions. A research paper of a theoretical nature is developed by the student and presented in the group. Prerequisites: Senior status in major or permission of the instructor; Offered as needed.

Prequisites: None

2
MAT 410

Number Theory

Number Theory is an introductory course in number theory, divisibility, congruences, Diophantine equations,continued fractions and Gaussian Integers. Prerequisites: MAT 126 and MAT 300

Prequisites: MAT-126 MAT-300

3
MAT 412

General Topology

This course covers metric spaces, continuous mappings, topological spaces, compactness, separation and connectedness. Prerequisites: MAT 301

Prequisites: MAT-301

3
MAT 414

Complex Analysis

This course studies analytic functions, complex integration and infinite series. Prerequisites: MAT 202 and MAT 300

Prequisites: MAT-202 MAT-300

3
MAT 417

Introduction to Graph Theory

This course will provide a first introduction to the theories and applications of graphs. Topics covered in the course include basic definitions and examples, paths, cycles, trees, planarity, graph colorings, digraphs and matching.

Prequisites: Mat-126 Mat-300

3
MAT 420

Introduction to Linear Models

Method of least squares, correlation, residual analysis, multiple linear regression,and introduction to generalized linear models. Prerequisite: MAT 404 or permission of instructor.

Prequisites: MAT-404 or Permission of Instructor

3
MAT 421

Design of Experiments

Methods of designing, conducting, and analyzing experiments, overview of sampling methods, sampling distributions, ANOVA, sample size calculations, nonparametric methods, randomized blocks, Latin squares, factorial designs, and the random effects model.

Prequisites: MAT-404 or Permission of Instructor

3
MAT 424

Numerical Analysis

Numerical solutions to the applications of calculus and linear algebra are covered in this course. Economic and scientific interpretations of functions are stressed. Prerequisites: MAT 126 and either CSC 151 or IT 111.

Prequisites: MAT-126, CSC-151 or IT-111

3
MAT 443

Methods of Teaching Mathematics

This course covers current issues in mathematics education, secondary school mathematics curricula and contemporary approaches to the teaching of mathematics.

Prequisites: Mat-126 Mat-300

3
MAT 479

Data Analysis Methods

Topics will be chosen by the instructor.

Prequisites: Mat-126 Mat-300

3
MAT 480

Statistical Applications

Topics will be chosen by the instructor.

Prequisites: MAT-126 MAT-300 MAT-479

3

SUBTOTAL: 9

In other academic areas required for major:

Select one of the following two sequences:

Course Number Course Name Credits
PHY 101

General Physics I

This calculus-based course is an introduction to the principles of kinematics and dynamics as they apply to both translational and rotational motion. Topics include Newton's laws, forces, friction, gravity, Kepler's laws, dot products and cross products, potential and kinetic energy, and momentum. Considerable attention is paid to the intellectual history that accompanied the emergence of the Newtonian world view.

Prequisites: Mat-125, Phy-101L

3
PHY 101L

Gen Physics Lab I



Prequisites: None

1
PHY 102

General Physics

This course is a continuation of PHY 101. The course covers statics, fluids, oscillations, sound and waves, temperature and heat, electricity and magnetism, and geometric optics.

Prequisites: Phy-101, Mat-126, Phy-102L

3
PHY 102L

Gen Physics Lab II

This course is a physics laboratory to accompany PHY 103. The course includes experiments in mechanics and oscillatory motion.

Prequisites: None

1

OR

Course Number Course Name Credits
PHY 103

Physics for Engineers

This course is a calculus-based introductory course in physics enriched in material of relevance to computer science, information technology and engineering students,including kinematics,Newtonian mechanics,momentum,energy,rotational motion,statics,materials, fluids and oscillatory motion.

Prequisites: Mat-125, Phy-103L

3
PHY 103L

Physics for Engineers Lab 1

This course is a physics laboratory to accompany Phy 103. The course includes experiments in mechanics and oscillatory motion.

Prequisites: Mat-125 Phy-103, Mat-125 Phy-103

1
PHY 104

Physics for Engineers II

This course is a continuation of PHY 103 and is a calculus-based introductory course in physics enriched in material of relevance to computer science information technology, and engineering students, including: wave motion, thermodynamics, heat transfer electricity, circuits and circuit components, magnetism, electromagnetic radiation and optics.

Prequisites: Phy-103, Mat-126, Phy-104L

3
PHY 104L

Physics for Engineers II Lab

This physics laboratory accompanies PHY 104. Experiments in wave motion, thermodynamics, electricity, magnetism and optics are performed

Prequisites: Mat-125 Phy-103, Phy-104

1

SUBTOTAL: 8

Major requirements: 44
Core requirements: 46
Free electives (including core electives): 30
Total: 120

Regulations

Program Requirements

Students within the department must maintain a minimum 2.0 G.P.A. in coursework required for their major and taken at D’Youville College. Students must have a minimum grade of B- in MAT 125 and MAT 126. Students who fail to earn this G.P.A. will be placed on probation in the major. Probation may continue for a maximum of three consecutive semesters or a total of four non- consecutive semesters. Students who exceed these limits will be dismissed from the major. Students may appeal these decisions on academic status by submitting, in writing to the department chairperson, reasons why exceptional consideration may be justified.

For students wishing to enter the master's program in education/ certification in education: The education program will allow up to three graduate courses to be taken while the student is an undergraduate. If a student wishes to take the entire three courses, two must fall in the senior’s final semester as an undergraduate. Further, it is expected that all juniors and seniors wishing to take graduate courses show substantial evidence of academic progress toward their undergraduate degree. Students may not take graduate courses in lieu of required courses by the program. Students must maintain a 2.75 G.P.A. to take graduate courses.

Admissions

Admission Requirements

The B.S. in mathematics requires a minimum SAT score of 1100 (Math and Verbal) (or ACT of 24), a high school average of 85 percent and a rank in the top 25 percent of one’s class. Transfer students are required to have a minimum G.P.A. of 3.0.

The B.A. in mathematics requires a minimum SAT score of 1000 (Math and Verbal) (or ACT of 21), a high school average of 85 percent and a rank in the top 50 percent of one’s class. Transfer students are required to have a minimum G.P.A. of 2.5.

Students nearly meeting these requirements will be considered for these programs by the department. Students denied immediate acceptance into the mathematics B.S. will be accepted in to the mathematics B.A. program if they meet its requirements. These students may be promoted into the mathematics B.S. program after they have sufficiently demonstrated competence (usually after the completion of two semesters).

Department

Department of Biology and Mathematics

Knowledge of science and mathematics is essential to the development of a liberally educated person. The student with a special interest in biology and mathematics will find a foundation for a wide variety of professional careers. These career opportunities are expanding rapidly in today’s increasingly technological society.

The community of scholars that comprises the faculty of math and natural sciences is committed to excellence in teaching, learning and research. The Biology and Mathematics department faculty encourage scholarship, skeptical inquiry and the free exchange of ideas within the department and in the classroom and laboratory, and promote the application of this knowledge beyond those settings. The department seeks to foster these principles in every one of its students, regardless of academic background, in ways that can both be measured and defy measurement.

All D'Youville students take some science and mathematics courses within the department. The department offers two bachelor’s degrees in biology and two in mathematics. Requirements for these programs are listed in the courses of instruction section of this catalog. The department offers structured minors in analytics, anatomy, bioinformatics, biology, environmental science, mathematics and natural sciences. The department also provides the basic science courses for many programs, including nursing, physician assistant, physical therapy, chiropractic, liberal studies in education and occupational therapy.

Students within the department must maintain a minimum 2.0 grade point average in courses taken at D’Youville in their subject area.