## Mathematics - BS

The major in Mathematics introduces students to a field whose origins date from the dawn of history and whose ever-increasing pervasiveness and importance in science, engineering, business and finance renders it a veritable master-key to our understanding of the world about us. The degree in mathematics opens many doors to students upon graduation to a job in business, industry or government, to certification as a teacher, to graduate study in mathematics, statistics and computer science, among many other fields to a professional school in business or law. Moreover, the major in mathematics serves as a gateway not only to a job or career, but also to a world where logic and imagination combine to create timeless beauty and truth.

What distinguishes the BS from the BA in Mathematics is the requirement of 7 credits in Computer Science and that of 4 additional credits in Physics. Although the number of general-elective credits is thereby reduced by 11, the remaining 21 credits could still allow for a minor in many fields.

To complete the mathematics major, a minimum of 120 credits is required, the last 30 of which must be earned at La Roche University. The required course work consists of the following:

- 46 credits in the mathematics core
- 7 credits in Computer Science
- 12 credits in Physics
- 37 credits in CORE Curriculum courses
- 18 credits of General Electives

### Summary of Requirements

#### Computer Science: 7 credits

- CSCI1002INTRO TO COMPUTER SCIENCE
### CSCI1002

INTRO TO COMPUTER SCIENCE#### Credits (Min/Max): 3/3

This course is an introduction to the field of Computer Science (CS). A scientific foundation of many aspects of CS will be developed upon which more advanced CS courses will build. Technical topics may include: computer design, information processing, algorithm concepts, operating systems, cyber security and networking and the internet. The evaluation of issues such as Artifical Intelligence & Ethics, Internet of Things (IoT), Big Data and Impact of Technology on Social Development Skills may also be included.

#### PREREQUISITES:

- CSCI1010PROGRAMMING I
### CSCI1010

PROGRAMMING I#### Credits (Min/Max): 3/3

This course introduces the art of algorithm design and problem solving in the context of computer programming. The basic structure and logic of the Java language is presented. Topics covered include data types and operators, control flow, repetition and loop statements, arrays and pointers. Good programming practices will be taught and encouraged.

#### PREREQUISITES:

*CSCI1002 or SLSC1005 or SLSC1012 & Concur: CSCI1010L* - CSCI1010LPROGRAMMING I - LAB
### CSCI1010L

PROGRAMMING I - LAB#### Credits (Min/Max): 1/1

Lab work for CSCI1010 Programming I.

#### PREREQUISITES:

#### Mathematics Core: 46 credits

- MATH1032ANALYTIC GEOMETRY AND CALCULUS I
### MATH1032

ANALYTIC GEOMETRY AND CALCULUS I#### Credits (Min/Max): 4/4

The first semester of a three-semester integrated course in the elements of analytic geometry and differential and integral calculus. Included are the concept and applications of the derivative of a function of a single variable, differentiation of polynomials and the trigonometric functions, the chain, product and quotient rules, implicit differentiation, and differentials. Concludes with anti-differentiation, integration, area under graphs of functions and applications.

#### PREREQUISITES:

*MATH1010* - MATH1033ANALYTIC GEOMETRY AND CALCULUS II
### MATH1033

ANALYTIC GEOMETRY AND CALCULUS II#### Credits (Min/Max): 4/4

A continuation of MATH1032 including applications of the definite integral, area, arc length, volumes and surface area, centroids, average value and theorem of the mean for definite integrals. Derivatives and integrals of transcendental functions are followed by techniques of integration, L'Hopital's Rule and indeterminate forms and improper integrals. Also included are conic sections and polar coordinates.

#### PREREQUISITES:

*MATH1032* - MATH2030ANALYTIC GEOMETRY AND CALC III
### MATH2030

ANALYTIC GEOMETRY AND CALC III#### Credits (Min/Max): 4/4

A continuation of MATH1033 including a study of vectors, parametric equations, solid analytic geometry and functions of several variables. Includes partial differentiation, total differentials, multiple integrals and surface and line integrals, the theorems of Gauss and Stokes, and infinite series.

#### PREREQUISITES:

*MATH1033* - MATH2031ORDINARY DIFFERENTIAL EQUATIONS
### MATH2031

ORDINARY DIFFERENTIAL EQUATIONS#### Credits (Min/Max): 3/3

A study of first and second order differential equations, infinite series, Laplace transforms and power series together with existence of solution and uniqueness theorems.

#### PREREQUISITES:

*MATH2030* - MATH2050DISCRETE MATHEMATICS I
### MATH2050

DISCRETE MATHEMATICS I#### Credits (Min/Max): 3/3

A basic course dealing with mathematics applicable to computer science. It provides an introduction to mathematical methods and covers such topics as: enumeration, set theory, mathematical logic, proof techniques, number systems, functions and relations, graphs and digraphs, trees, combinatorics, basic algebraic structures, recurrence relations, Boolean algebra, and analysis of algorithms.

#### PREREQUISITES:

*MATH1032* - MATH2051DISCRETE MATHEMATICS II
### MATH2051

DISCRETE MATHEMATICS II#### Credits (Min/Max): 3/3

A continuation of MATH1014. Topics to be covered will include some or all of the following: integers and integers Mod n; counting techniques, combinatorics, and discrete probability; graphs, trees, and relations; Boolean algebras; and models of computation such as grammars, finite-state machines, and Turing machines.

#### PREREQUISITES:

*MATH2050* - MATH3015LINEAR ALGEBRA
### MATH3015

LINEAR ALGEBRA#### Credits (Min/Max): 3/3

A development of the theory of vector spaces from linear equations, matrices and determinants. Topics include linear independence, bases, dimensions, linear mappings, orthogonal reduction, diagonalization of matrices using eigenvectors and eigenvalues.

#### PREREQUISITES:

- MATH3040PROBABILITY AND STATISTICS I
### MATH3040

PROBABILITY AND STATISTICS I#### Credits (Min/Max): 3/3

A calculus-based first course in probability and statistics for science and honors students. Various discrete and continuous probability distributions will be examined including the binomial, multinomial, Poisson, uniform, exponential, gamma and normal distributions. Mathematical expectation, moment generating functions, linear combinations of random variables, sampling distributions, point estimation, confidence intervals, hypothesis testing, analysis of variance, regression, correlation and the method of least squares will also be examined.

#### PREREQUISITES:

- MATH3045PROBABILITY AND STATISTICS II
### MATH3045

PROBABILITY AND STATISTICS II#### Credits (Min/Max): 3/3

A detailed study of topics in statistics: comparison of classical and Bavesian methods in conditional probability and estimation of parametrics, non-linear regression, multiple, partial and rank correlation, indices, time series, analyses of variance for two-way classification with and without interaction, design of experiments, reliability and validity of measurements and non-parametric tests.

#### PREREQUISITES:

*MATH3040* - MATH4003HISTORY OF MATHEMATICS
### MATH4003

HISTORY OF MATHEMATICS#### Credits (Min/Max): 3/3

A survey course in the development of modern mathematics. Beginning with the rudimentary mathematical concepts developed in prehistoric times, mathematics grew sometimes slowly and sometimes rapidly with the insights of various cultures. In this course we trace this development through ancient Mesopotamia and Egypt, classical Greece, Arabic and Hindu cultures of the Dark and Middle Ages, the European Renaissance and on into the modern times. Special attention will be paid to major developments such as the emergence of mathematics as an organized, reasoned and independent discipline in Classical Greece; the emergence and development of major areas of mathematics such as of algebra, trigonometry, productive geometry, calculus, analytic geometry infinite series, non-Euclidean geometry; and how developments in mathematical thought have shaped the modern world.

#### PREREQUISITES:

*MATH2031* - MATH4015MODERN ABSTRACT ALGEBRA
### MATH4015

MODERN ABSTRACT ALGEBRA#### Credits (Min/Max): 3/3

An introduction to algebraic concepts such as groups, rings, integral domains and fields. The elementary number systems occupy a central place. Mappings, especially homorphisms, are introduced early and emphasized through out the course.

#### PREREQUISITES:

- MATH4020GEOMETRY
### MATH4020

GEOMETRY#### Credits (Min/Max): 3/3

An overview of geometry in the light of modern trends with attention to axiomatic structure, including an introduction to hyperbolic and elliptic figures as geometric structures together with an overview of projective geometry.

#### PREREQUISITES:

*MATH2030* - MATH4035REAL ANALYSIS
### MATH4035

REAL ANALYSIS#### Credits (Min/Max): 3/3

An introductory to classical (real) analysis. Includes a rigorous treatment of logic, set theory, functions, countable and uncountable sets, the real number system, metric spaces, sequences, series, differentiation and integration.

#### PREREQUISITES:

*MATH2031* - MATH4090JR/SR SEMINAR IN MATHEMATICS
### MATH4090

JR/SR SEMINAR IN MATHEMATICS#### Credits (Min/Max): 1/1

The weekly one-hour seminar treats of a topic or of topics important in applied and/or theoretical mathematics. The specific topic or topics may vary from year to year. Topics in the past have included actuarial mathematics, the Millennium Problems, and the Riemann Hypothesis.

#### PREREQUISITES:

*MATH2031 & MATH3015*

#### Physics: 12 credits

- PHYS1032GENERAL PHYSICS I
### PHYS1032

GENERAL PHYSICS I#### Credits (Min/Max): 3/3

This is the first of a three-semester introduction to calculus-based physics stressing experimental and problem-solving techniques. Concepts covered are mechanics, kinematics, Newton's laws of motion, conservation laws, rotational motion, gravitation, oscillation, and wave/acoustics.

#### PREREQUISITES:

*MATH1032, Coreq: PHYS1032L* - PHYS1032LGENERAL PHYSICS I - LAB
### PHYS1032L

GENERAL PHYSICS I - LAB#### Credits (Min/Max): 1/1

Laboratory for PHYS1032 General Physics I

#### PREREQUISITES:

- PHYS1033GENERAL PHYSICS II
### PHYS1033

GENERAL PHYSICS II#### Credits (Min/Max): 3/3

The second of a three-semester introduction to calculus-based physics. Concepts covered are thermal properties and electromagnetism: thermo dynamics, electricity, magnetism, electromagnetic wave, geometrical optics, and physics optics.

#### PREREQUISITES:

*PHYS1032, Coreq: PHYS1033L* - PHYS1033LGENERAL PHYSICS II - LAB
### PHYS1033L

GENERAL PHYSICS II - LAB#### Credits (Min/Max): 1/1

Laboratory for PHYS1033 General Physics II

#### PREREQUISITES:

- PHYS2030GENERAL PHYSICS III
### PHYS2030

GENERAL PHYSICS III#### Credits (Min/Max): 3/3

The third of a three-semester introduction to calculus-based physics. This course is devoted to the study of the two great theories that underlie almost all of modern physics, quantum theory and relativity theory. There is an emphasis on quantum mechanical description of semiconductor physics, which forms our modern electronics age (computers and electronic communication devices in general). A series of laboratory projects enables the student to retrace experimentally the development of modern physics.

#### PREREQUISITES:

*PHYS1033, Coreq: PHYS2030L* - PHYS2030LGENERAL PHYSICS III - LAB
### PHYS2030L

GENERAL PHYSICS III - LAB#### Credits (Min/Max): 1/1

Laboratory for PHYS2030 General Physics III

#### PREREQUISITES:

*PHYS1033L*