# Mathematics

## Mathematics Major

### Degree Requirements - 126 credits

Students can earn a bachelor of arts degree with this major.  See the requirements for the bachelor of arts degree.

Students can earn a bachelor of science degree with this major.  See the requirements for the bachelor of science degree.

### Major Requirements: 15-16 courses, 53-57 credits

The major in Mathematics consists of the following required core courses plus ONE of the concentrations listed below.

#### Introductory Requirement (1 course, 4 credits)

Choose one of the following:

#### MATH-164 Calculus 1 Bridge With Trigonometry

Prerequisites:

Permission of Instructor

Credits:

4

Description:

This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.

#### MATH-165 Calculus I

Prerequisites:

MATH-121 with a minimum grade of C, MATH-075, or MATH level 5

Credits:

4

Description:

Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-166 Calculus II

Prerequisites:

MATH-164 or MATH-165 with a minimum grade of C

Credits:

4

Description:

Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-185 Discrete Mathematics I

Prerequisites:

Take MATH-121, MATH-164, MATH-165, or MATH-166

Credits:

4

Description:

Topics covered include: Logic and set theory, basic techniques of proof, relations and functions and their properties (equivalence relations, partial order relations, recurrence relations and their solutions), cardinality, elementary number theory, mathematical induction, counting, Pigeonhole principle, discrete probability. Normally taken second semester freshman year.

#### MATH-265 Calculus III

Prerequisites:

MATH 166 with grade of C or better

Credits:

4

Description:

Parametric equations and polar coordinates (curves, areas, conic sections); vectors and the geometry of space (the dot product, vector arithmetic, lines and planes in 3-space, the cross product, cylinders and quadratic surfaces); vector functions (limits, derivatives and integrals, motion in space); partial derivatives (functions of several variables, limits and continuity, tangent planes and differentials, chain rule, directional derivatives, gradient, extrema, Lagrange multipliers); multiple integrals (double integrals, applications); vector calculus (vector fields, line integrals, fundamental theorem for line integrals, Green's Theorem, curl and divergence, parametric surfaces, surface integrals). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-331 Introduction to Advanced Mathematics

Prerequisites:

Take MATH-185 with a grade of C or better

Credits:

4

Description:

this course is intended to provide a firm foundation for and a taste of the study of advanced mathematics. While the course content varies somewhat, it is designed to give students a deeper understanding of the algebraic and analytical structure of the integers, the rational numbers and the real numbers and how they act as a building block to a variety of fields of mathematics. Students are introduced to the process of mathematical discovery and the language of mathematics. Exercises and projects are designed to illustrate the need for proof and to further refine the student's ability to analyze, conjecture and write mathematical proofs. This course is a prerequisite for most upper level mathematics courses and, after completing it a student will be in a position to determine realistically if he or she ought to major or minor in mathematics.

#### MATH-431 Linear Algebra

Prerequisites:

Math 331 must have grade C or higher

Credits:

4

Description:

System of linear equations, Gaussian elimination, matrices and their algebra, inverse of a matrix, determinants, cofactor expansion, Cramer's rule, vectors in and their algebra, abstract vector spaces, subspaces, linear independence, basis and dimension, linear transformations, isomorphism of vector spaces, rank and nullity, matrix of a linear transformation, inner product spaces, angle and orthogonality, eigenvalues and eigenvectors of a linear transformation, characteristic equation, Cayley-Hamilton theorem, diagonalization.

#### MATH-462 Real Analysis

Prerequisites:

MATH 331 with at least a grade of C

Credits:

4

Description:

A detailed treatment of the basic concepts of analysis including the real numbers; completeness and its equivalence to other properties of the reals such as monotone convergence, Archimedean property, Bolzano-Weierstrass theorem; the topology of Euclidean spaces, compactness and the Heine-Borel theorem, connectedness, continuity and uniform continuity and uniform continuity, pointwise and uniform convergence of functions, and an introduction to metric spaces.

#### MATH-511 Launching a Career in Mathematics

Prerequisites:

Junior or Senior standing

Credits:

1

Description:

This team-taught course is designed to explore career opportunities in Mathematics in depth. This course focuses on career search, the application process, entry, transition and networking for career success. Alternative options such as graduate school will also be explored. Students articulate and reflect on academic work, and co-curricular experiences from the perspective of professionals entering or advancing their careers. The goal of this course is to help students reach their fullest professional potential following graduation.

#### CMPSC-F131 Computer Science I

Prerequisites:

MATH placement 3 or higher, MATH-121, MATH-164, or MATH-165 (previous or concurrent)

Credits:

4

Description:

This is a rigorous introduction to computer science in Java with an emphasis on problem solving, structured programming, object-oriented programming, and graphical user interfaces. Topics include expressions, input/output, control structures, intrinsic data types, classes and methods, iteration, top-down programming, arrays, graphical user interfaces, and elements of UML. Normally offered each semester.

#### Concentration Requirement

Students must complete the requirements of one of the following concentrations:

1. Concentration in Actuarial Science (7 courses, 24 credits)
2. Concentration in Pure Math (6 courses, 20 credits)

Residency Requirement Policy: In the College of Arts and Sciences, a two-course (8 credit) residency requirement must be satisfied for completion of a minor and a four-course (16 credit) residency requirement must be satisfied for the completion of a major.

## Actuarial Science Concentration

### Actuarial Science Concentration: 7 courses, 24 credits

#### EC-101 Applied Microeconomics

Prerequisites:

Non CAS majors need to have completed at least 15 credits.

Credits:

3

Description:

This course introduces students to foundational principles of microeconomic theory, with an emphasis on applications of concepts to management decision-making in specific industry and market settings. It describes and analyzes the interaction of supply and demand and the behavior of the prices of goods, services. It explains the determinations of costs, output, strategic pricing, and governance by firms under conditions of perfect and imperfect competition in a global economy. In addition, it describes the supply demand for factors of production and the impact of taxes and government regulation and intervention on firms and consumers.

#### EC-102 Global Macroeconomics

Prerequisites:

Non-CAS majors need to have completed at least 15 credits

Credits:

3

Description:

This course examines the workings of the national and the global economy. It will describe the determination of Gross Domestic Product, the problems of unemployment, inflation, and the determination of economic growth. It will also describe and analyze the determination of the country's exchange rate, the balance of payments, and international borrowing and lending. A particular focus will be on understanding economic fluctuations (booms, busts, and recessions) in the domestic economy and its effects on other economies. It will analyze the role of the government and the effects of government spending and taxation on the economy. Furthermore, it will describe and analyze the determination of the quantity of money and interest rates in the economy and the role of the country's central bank. It examines the basis and pattern of international trade and the effects of a country's trade policy on the economy.

Prerequisites:

ACCT-201, MATH-128 or higher, and STATS-240 or STATS-250 (can be taken concurrently with FIN-200); Sophomore standing

Credits:

3.00

Description:

This course is a study of the functions of business finance and focuses on basic financial principles such as time value of money, risk and return tradeoffs, and asset valuation. Formally FIN 310.

#### MATH-255 Probability and Statistics

Prerequisites:

MATH-165 or MATH-164 with a grade of C or better

Credits:

4

Description:

Topics include: random variable and distribution; expectation and variance; special discrete/continuous distributions (uniform, binomial, negative binomial, geometric, hypergeometric, Poisson, normal, and exponential distributions); joint distribution, marginal distribution and conditional distribution; covariance; limit theorems (law of large numbers and central limit theorem); introduction to confidence interval and hypothesis testing; regression analysis. Offered as needed.

#### MATH-290 Financial Mathematics I

Prerequisites:

MATH-166, 164 or 165 with a minimum grade of C

Credits:

4

Description:

This course is mainly designed for students who are interested in financial mathematics and/or actuarial sciences, especially if they plan to take the second actuarial exam, and/or if they plan to study more in financial mathematics. The materials covered include time value of money, annuities, loans, bonds, cash flows and portfolios, general derivatives, options, hedging and investment strategies, forwards and futures, and swaps.

#### MATH-357 Math Statistical Analysis

Prerequisites:

MATH-255 with a minimum C grade

Credits:

4

Description:

Calculus based introduction to statistical analysis. Topics include sampling distribution, point estimation, interval estimation, hypothesis testing, regression and correlation analysis.

#### Concentration Elective (1 course, 3 credits)

Choose one of the following:

#### FIN-311 Intermediate Finance

Prerequisites:

FIN-200

Credits:

3

Description:

Intermediate Finance expands on basic financial concepts and introduces more advanced topics. Material emphasizes solutions to problems of capital structure, investment and financing. Other major topics include distribution policy, working capital management, derivative corporate securities, and corporate restructuring.

#### FIN-313 General Insurance

Prerequisites:

FIN 200 (formerly FIN 310); Junior standing

Credits:

3

Description:

This course includes the theory, practice and problems of risk bearing in business and personal pursuits including life, property and casualty insurance and dealing with contract analysis and investments as well as corporate risk management.

#### FIN-315 Principles of Investments

Prerequisites:

FIN 200 and Junior standing

Credits:

3

Description:

This course covers the investment of funds by individuals and institutions. Focuses on analysis of investments and security markets, and the mechanics of trading and investing. A variety of investment vehicles are discussed, including stocks, bonds, futures, and options.

#### FIN-411 Futures and Options

Prerequisites:

FIN 315; Junior standing;

Credits:

3

Description:

This course is an in-depth analysis of derivatives: futures, options, and swaps. The course explains why these securities exist, where and how they are traded, how to employ them in managing risk, and how to accurately price them. It also covers the use of these derivatives in the context hedging or speculation.

#### FIN-413 Investment Analysis and Portfolio Management

Prerequisites:

FIN 315, Junior standing

Credits:

3

Description:

This course is an advanced course in investment analysis stressing efficient frontier and diversification. Also studies portfolio construction and management, and the tradeoff of risk versus return.

Courses required in the major follow recommendations of the Society of Actuaries (SOA). Some Economics and Finance courses contribute to the Validation by Educational Experience (VEE) recommendations of the SOA.

Note: Although not required, it is strongly recommended that Mathematics majors also take CMPSC-F132 Computer Science II and an internship in Mathematics.

### Mathematics Actuarial Science Learning Goals & Objectives

Learning goals and objectives reflect the educational outcomes achieved by students through the completion of this program. These transferable skills prepare Suffolk students for success in the workplace, in graduate school, and in their local and global communities.

Learning Goals Learning Objectives
Students will...
Students will be able to...
Strengthen their problem-solving skills and further develop their mathematical maturity
• Make use of reasoning along with suitable theorems, ideas, or methods of proof to solve problems and prove mathematical facts
• Correctly implement suitable algorithms and perform multi-step computations
• Interpret and evaluate the practical merits of computed answers
• Understand, evaluate, and interpret quantitative information given in a variety of formats
• Make estimates and apply data given in graphical, tabular, or algebraic formats, and translate data between various formats
• Sketch graphs of given formulaic relationships with input from calculus, and identify and interpret graphical representations
• Understand the need for proof and what comprises mathematical proof
• Correctly apply techniques of logic and abstract reasoning in formulating and proving statements
• Read, write and understand proofs, and evaluate the correctness of a given proof
• Use various proof techniques successfully
• Have a working knowledge of foundational technical material
• Understand and express the statements of key theorems, and identify the main ideas in the proofs of certain of these theorems
• Analyze various mathematical situations and codify them in suitable mathematical language
• Understand and express conceptual motivations for computations
• Know how to frame appropriate real-world problems in mathematical language
• Use data in various forms to set up an abstract mathematical version of a problem
• Translate between information in practical real-world scenarios and the mathematical context, and back
• Recognize real-world manifestations of concepts from calculus and other mathematical disciplines, and problems to which these subjects can be applied
• Skillfully communicate (both orally and in writing) mathematical ideas and applications
• Explain mathematical processes and computations to others (both mathematicians and a general audience), orally or in writing
• Collaborate with others in the formulation, solution, and presentation of a [calculus, etc.] problem
• Use professional and domain-specific terminology correctly
• Demonstrate competency in probability and financial mathematics
• Show solid understanding and apply common distributions (binomial, Poisson, Normal, exponential)
• Work with joint distributions, and identify linear relations between two random variables
• Demonstrate solid understanding of central limit theorem and apply it
• Show solid understanding and apply the theory of interest

• ## Pure Mathematics Concentration

### Pure Mathematics Concentration: 6 courses, 20 credits

#### MATH-432 Abstract Algebra

Prerequisites:

MATH 431

Credits:

4

Description:

An introduction to elementary group theory, including properties of groups, subgroups, first isomorphism theorem for groups, normal subgroups, finite group classification; elementary properties of rings, such as homomorphisms of rings, ideals, fields, Euclidean algorithm, rings of polynomials, factorization theory, integral domains, associates, primes and units in domains, and other topics in number theory. Prerequisite: MATH 431 with a grade of C or higher.

#### PHYS-151 University Physics I

Prerequisites:

MATH-121 or higher (previously or concurrently) and PHYS L151 concurrently

Credits:

3

Description:

PHYS 151 is the first of three courses (PHYS 151, 152, 153) that comprise the calculus based introductory physics sequence at Suffolk University intended for students majoring in the physical sciences, engineering and mathematics. This course aims to teach basic techniques in physics that fall under the topic of classical mechanics and their application in understanding the natural world. Specific topics include the study of vectors, Newton's laws, rotations, rigid body statics and dynamics, fluid mechanics, simple harmonic motion, mechanical waves, sound and hearing. The student will learn how to analyze physical situations by using simple models, and also how to solve those models and derive useful conclusions from them. This course will show students how experimental results and mathematical representations are combined to create testable scientific theories, and how the complexities of most real-life physical situations can be reduced to simple problems by identifying the essential physical features and ignoring the rest. The student will learn to distinguish the scientific approach to physical situations from other ways of looking at them, for example, artistic, humanistic, and business.

#### PHYS-L151 University Physics Lab I

Prerequisites:

MATH 121 or higher (previously or concurrently) PHYS 151 concurrently

Credits:

1

Description:

The laboratory consists of experiments to illustrate the basic concepts studied in the course: measurements, propagation of errors, vectors, Newton's laws, work and energy, momentum, rotations, oscillations, simple harmonic motion, fluid. Knowledge of algebra, trigonometry, differentiation and integration required.

#### Concentration Electives (3 courses, 12 credits)

Choose two additional 4-credit Math courses at the 200-level or higher

Choose one additional 4-credit Math course at the 300-level or higher

Note: Although not required, it is strongly recommended that Mathematics majors also take CMPSC-F132 Computer Science II and an internship in Mathematics.

#### Pure Mathematics Learning Goals & Objectives

Learning goals and objectives reflect the educational outcomes achieved by students through the completion of this program. These transferable skills prepare Suffolk students for success in the workplace, in graduate school, and in their local and global communities.

Learning Goals Learning Objectives
Students will...
Students will be able to...
Strengthen their problem-solving skills and further develop their mathematical maturity
• Make use of reasoning along with suitable theorems, ideas, or methods of proof to solve problems and prove mathematical facts
• Correctly implement suitable algorithms and perform multi-step computations
Interpret and evaluate the practical merits of computed answers
• Understand, evaluate, and interpret quantitative information given in a variety of formats
• Make estimates and apply data given in graphical, tabular, or algebraic formats, and translate data between various formats
• Sketch graphs of given formulaic relationships with input from calculus, and identify and interpret graphical representations
• Understand the need for proof and what comprises mathematical proof
• Correctly apply techniques of logic and abstract reasoning in formulating and proving statements
• Read, write and understand proofs, and evaluate the correctness of a given proof
• Use various proof techniques successfully
• Have a working knowledge of foundational technical material
• Understand and express the statements of key theorems, and identify the main ideas in the proofs of certain of these theorems
• Analyze various mathematical situations and codify them in suitable mathematical language
• Understand and express conceptual motivations for computations
• Know how to frame appropriate real-world problems in mathematical language
• Use data in various forms to set up an abstract mathematical version of a problem
• Translate between information in practical real-world scenarios and the mathematical context, and back
• Recognize real-world manifestations of concepts from calculus and other mathematical disciplines, and problems to which these subjects can be applied
• Skillfully communicate (both orally and in writing) mathematical ideas and applications
• Explain mathematical processes and computations to others (both mathematicians and a general audience) orally or in writing
• Collaborate with others in the formulation, solution, and presentation of a [calculus, etc.] problem
• Use professional and domain-specific terminology correctly
• ## Math Education Option

Students interested in Math Education should take the Math major with a concentration in Pure Math and minor in Educational Studies, choosing courses with the guidance of advisors.

## Actuarial Mathematics Minor

### Minor Requirements: 7 courses, 26 credits

#### Introductory Requirement (1 course, 4 credits)

Choose one of the following:

#### MATH-164 Calculus 1 Bridge With Trigonometry

Prerequisites:

Permission of Instructor

Credits:

4

Description:

This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.

#### MATH-165 Calculus I

Prerequisites:

MATH-121 with a minimum grade of C, MATH-075, or MATH level 5

Credits:

4

Description:

Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### EC-101 Applied Microeconomics

Prerequisites:

Non CAS majors need to have completed at least 15 credits.

Credits:

3

Description:

This course introduces students to foundational principles of microeconomic theory, with an emphasis on applications of concepts to management decision-making in specific industry and market settings. It describes and analyzes the interaction of supply and demand and the behavior of the prices of goods, services. It explains the determinations of costs, output, strategic pricing, and governance by firms under conditions of perfect and imperfect competition in a global economy. In addition, it describes the supply demand for factors of production and the impact of taxes and government regulation and intervention on firms and consumers.

#### EC-102 Global Macroeconomics

Prerequisites:

Non-CAS majors need to have completed at least 15 credits

Credits:

3

Description:

This course examines the workings of the national and the global economy. It will describe the determination of Gross Domestic Product, the problems of unemployment, inflation, and the determination of economic growth. It will also describe and analyze the determination of the country's exchange rate, the balance of payments, and international borrowing and lending. A particular focus will be on understanding economic fluctuations (booms, busts, and recessions) in the domestic economy and its effects on other economies. It will analyze the role of the government and the effects of government spending and taxation on the economy. Furthermore, it will describe and analyze the determination of the quantity of money and interest rates in the economy and the role of the country's central bank. It examines the basis and pattern of international trade and the effects of a country's trade policy on the economy.

#### MATH-166 Calculus II

Prerequisites:

MATH-164 or MATH-165 with a minimum grade of C

Credits:

4

Description:

Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-255 Probability and Statistics

Prerequisites:

MATH-165 or MATH-164 with a grade of C or better

Credits:

4

Description:

Topics include: random variable and distribution; expectation and variance; special discrete/continuous distributions (uniform, binomial, negative binomial, geometric, hypergeometric, Poisson, normal, and exponential distributions); joint distribution, marginal distribution and conditional distribution; covariance; limit theorems (law of large numbers and central limit theorem); introduction to confidence interval and hypothesis testing; regression analysis. Offered as needed.

#### MATH-290 Financial Mathematics I

Prerequisites:

MATH-166, 164 or 165 with a minimum grade of C

Credits:

4

Description:

This course is mainly designed for students who are interested in financial mathematics and/or actuarial sciences, especially if they plan to take the second actuarial exam, and/or if they plan to study more in financial mathematics. The materials covered include time value of money, annuities, loans, bonds, cash flows and portfolios, general derivatives, options, hedging and investment strategies, forwards and futures, and swaps.

#### MATH-357 Math Statistical Analysis

Prerequisites:

MATH-255 with a minimum C grade

Credits:

4

Description:

Calculus based introduction to statistical analysis. Topics include sampling distribution, point estimation, interval estimation, hypothesis testing, regression and correlation analysis.

Residency Requirement Policy: In the College of Arts and Sciences, a two-course (8 credit) residency requirement must be satisfied for completion of a minor and a four-course (16 credit) residency requirement must be satisfied for the completion of a major.

Minor Programs Policy: A student declaring a minor may use no more than two courses from a major or double major combination to fulfill the requirements for the minor. No more than one course from one minor may count toward the fulfillment of a second minor. Students may not minor in a subject in which they are also completing a major. For more information, see the Minor Programs section of the CAS Degree Requirements page.

## Pure Mathematics Minor

### Minor Requirements: 6 courses, 24 credits

#### Introductory Requirement (1 course, 4 credits)

Choose one of the following:

#### MATH-164 Calculus 1 Bridge With Trigonometry

Prerequisites:

Permission of Instructor

Credits:

4

Description:

This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.

#### MATH-165 Calculus I

Prerequisites:

MATH-121 with a minimum grade of C, MATH-075, or MATH level 5

Credits:

4

Description:

Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-166 Calculus II

Prerequisites:

MATH-164 or MATH-165 with a minimum grade of C

Credits:

4

Description:

Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-185 Discrete Mathematics I

Prerequisites:

Take MATH-121, MATH-164, MATH-165, or MATH-166

Credits:

4

Description:

Topics covered include: Logic and set theory, basic techniques of proof, relations and functions and their properties (equivalence relations, partial order relations, recurrence relations and their solutions), cardinality, elementary number theory, mathematical induction, counting, Pigeonhole principle, discrete probability. Normally taken second semester freshman year.

#### MATH-265 Calculus III

Prerequisites:

MATH 166 with grade of C or better

Credits:

4

Description:

Parametric equations and polar coordinates (curves, areas, conic sections); vectors and the geometry of space (the dot product, vector arithmetic, lines and planes in 3-space, the cross product, cylinders and quadratic surfaces); vector functions (limits, derivatives and integrals, motion in space); partial derivatives (functions of several variables, limits and continuity, tangent planes and differentials, chain rule, directional derivatives, gradient, extrema, Lagrange multipliers); multiple integrals (double integrals, applications); vector calculus (vector fields, line integrals, fundamental theorem for line integrals, Green's Theorem, curl and divergence, parametric surfaces, surface integrals). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-331 Introduction to Advanced Mathematics

Prerequisites:

Take MATH-185 with a grade of C or better

Credits:

4

Description:

this course is intended to provide a firm foundation for and a taste of the study of advanced mathematics. While the course content varies somewhat, it is designed to give students a deeper understanding of the algebraic and analytical structure of the integers, the rational numbers and the real numbers and how they act as a building block to a variety of fields of mathematics. Students are introduced to the process of mathematical discovery and the language of mathematics. Exercises and projects are designed to illustrate the need for proof and to further refine the student's ability to analyze, conjecture and write mathematical proofs. This course is a prerequisite for most upper level mathematics courses and, after completing it a student will be in a position to determine realistically if he or she ought to major or minor in mathematics.

#### Elective (1 course, 4 credits)

Choose one additional 4-credit Mathematics course at the 200-, 300-, or 400-level.

Residency Requirement Policy: In the College of Arts and Sciences, a two-course (8 credit) residency requirement must be satisfied for completion of a minor and a four-course (16 credit) residency requirement must be satisfied for the completion of a major.

Minor Programs Policy: A student declaring a minor may use no more than two courses from a major or double major combination to fulfill the requirements for the minor. No more than one course from one minor may count toward the fulfillment of a second minor. Students may not minor in a subject in which they are also completing a major. For more information, see the Minor Programs section of the CAS Degree Requirements page.

## Honors

To complete requirements for honors in the major, a candidate must:

1. Graduate with a major GPA of 3.5 or higher
2. Graduate with an overall GPA of 3.0 or higher
3. Complete one of the two following options:
1. Mathematics courses
1. Complete MATH-H500 with a grade of A- or higher
2. Complete a thesis, presentation, or project in MATH-H400 that is approved by the supervising faculty member
2. Actuarial Exam
1. A student must pass at least one of the Actuarial Exams given by the Society of Actuaries
4. CAS Honors Program students only: Present work from the senior honors experience at the Honors Symposium or Pecha Kucha event

To become a candidate for honors in the major, a student must:

1. Apply to the supervising faculty member by meeting and agreeing upon the topic of study and the scope of the project

CAS Honors Program students only: CAS Honors Program students are assumed to be candidates for departmental honors and should consult with a major advisor(s) during junior year about registering for major honors requirements as described above

All other students: Apply to their advisor and consult with their advisor to schedule classes as described above

#### MATH-H500 Honors Senior Project in Mathematics

Prerequisites:

Instructor consent required

Credits:

1.00- 4.00

Description:

Students study an advanced mathematics topic in depth. Work typically results in a project of significant depth and breadth.

## Mathematics Courses

#### MATH-000 Mathshop - Bridge to College Math

Credits:

0

Description:

A NON-CREDIT, full semester workshop designed for students who need substantial review before starting MATH 104, MATH 121, or MATH 128. Similar to a course, MATHSHOP meets three hours per week throughout the semester. Topics covered are tailored to the needs of students and include basic math material, basic algebra, use of calculators, ways of dealing with math fears, and study methods. Several sections normally offered each semester.

#### MATH-104 Precalculus for Management & Social Sciences

Prerequisites:

MATH level 2 or Mathshop

Credits:

4

Description:

A selection of topics in algebra and elementary analytic geometry including, (but not restricted to): properties of real numbers, linear equations and inequalities, absolute value equations and inequalities, polynomials, rational expressions, exponents and radicals, quadratic equations, functions, linear, quadratic and polynomial models, rational, exponential and logarithmic functions. Applications and graphs are stressed throughout the course. This course is intended to prepare students who have only had one year of high school algebra to take MATH 134. Students may not use this course alone to satisfy the C.A.S. math requirement. Qualifying math placement exam score required. Students who are not prepared for this course should take MATHSHOP. Several sections offered each semester. *This course cannot be applied toward a departmental concentration in Mathematics by Sawyer Business School students. This course cannot be taken for credit by a student who already has credit for a more advanced course.

#### MATH-121 Precalculus With Elements of Calculus

Prerequisites:

MATH-104 with a minimum grade of B or MATH level 4

Credits:

4

Description:

A review of topics in algebra, trigonometry and analytic geometry including (but not restricted to): graphs and transformations of functions; properties of polynomial, rational, radical, exponential, and logarithmic functions; solving quadratic, exponential, and logarithmic equations; conic sections; the unit circle and right angle trigonometry; graphs of trigonometric functions; inverse trigonometric functions; analytic trigonometry; trigonometric identities and trigonometric equations. Intended for students needing one additional semester of preparation before taking MATH 165. Students may not use this course alone to satisfy the CAS math requirement. Prerequisites: MATH 104 with B or higher or qualifying placement exam score indicating solid grounding in intermediate algebra. 4 lecture hours plus 1 recitation session per week. Normally offered every semester. *This course cannot be applied toward a departmental concentration in Mathematics by Sawyer Business School students. This course does not satisfy the core math requirement for CAS or SBS. This course cannot be taken for credit by a student who already has credit for a more advanced course.

#### MATH-128 Math for the Modern World

Prerequisites:

MATH level 2, or Mathshop, or MATH-104

Credits:

4

Description:

From the ISBN on a book, to buying a car, from the size of small chips in a cell phone, to the size of the national debt, or just reading a graph in the daily newspaper, mathematics plays an important and vital role in countless areas of life and your future career and courses included. Mathematics is both an art and a tool created by humans. The common bond is a way of thinking and a way of reasoning to describe and solve problems of many types. This course uses the context of modern real life problems to introduce math needed for literacy and problem solving in contemporary life and work. It uses a minimal amount of algebra and focuses on math models, concepts and basic math manipulations. It encourages students to move from anxiety about math, to using formulas well, to thinking critically in the math context to use math to solve problems and pose new problems. Topics include scientific notation, basic financial math, linear, exponential and polynomial models and an introduction to probability. (Formerly Math 132)

#### MATH-130 Topics in Finite Mathematics

Prerequisites:

MATH-104, or MATH-121, or MATH level 3

Credits:

4

Description:

Linear Modeling (for example, using linear functions to model supply/demand situations), graphing, linear programming, financial functions (compound interest, annuities, and amortization of loans) sets, Venn diagrams, counting and combinatorics, discrete probability, conditional probability, Bernoulli experiments, Bayes theorem. Several sections offered each semester. *This course cannot be applied toward a departmental concentration in Mathematics by Sawyer Business School students.

#### MATH-134 Calculus for Management & Social Sciences

Prerequisites:

MATH-104, MATH-121 or MATH level 4

Credits:

4

Description:

A one-semester introduction to differential and integral calculus. Theory is presented informally and topics and techniques are limited to polynomials, rational functions, logarithmic and exponential functions. Topics include a review of precalculus, limits and continuity, derivatives, differentiation rules, applications of derivatives to graphing, minima/maxima, applications of the derivative, marginal analysis, differential equations of growth and decay, anti-derivatives, the definite integral, the Fundamental Theorem of Calculus, and area measurements. This course cannot be used to satisfy core or complementary requirements by students majoring in chemistry, computer science, engineering, mathematics, or physics. Several sections offered each semester.

#### MATH-164 Calculus 1 Bridge With Trigonometry

Prerequisites:

Permission of Instructor

Credits:

4

Description:

This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.

#### MATH-165 Calculus I

Prerequisites:

MATH-121 with a minimum grade of C, MATH-075, or MATH level 5

Credits:

4

Description:

Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-166 Calculus II

Prerequisites:

MATH-164 or MATH-165 with a minimum grade of C

Credits:

4

Description:

Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-185 Discrete Mathematics I

Prerequisites:

Take MATH-121, MATH-164, MATH-165, or MATH-166

Credits:

4

Description:

Topics covered include: Logic and set theory, basic techniques of proof, relations and functions and their properties (equivalence relations, partial order relations, recurrence relations and their solutions), cardinality, elementary number theory, mathematical induction, counting, Pigeonhole principle, discrete probability. Normally taken second semester freshman year.

#### MATH-200 Modern Mathematics and Career Exploration

Prerequisites:

Freshman or Sophomore Status

Credits:

1

Description:

This one credit course aims to help freshmen and sophomore students form an idea of the scope of the vast and rapidly growing field of mathematics and the many career options, and begin to map out steps toward a potential career path. Mathematics is a diverse discipline that is constantly evolving. It ranges from applied mathematics (tailored to specific real world problems), to mathematical physics (which crafts the mathematical basis for the understanding of physical phenomena), to pure mathematics (which is studied for its intrinsic interest). As the study of such varied concepts as quantity, structure, space and change, mathematics has something for everyone; and valuable applications to many other fields, from business and finance to meteorology, chemistry, ecology and biology, among many others. This module aims to move beyond the foundational math generally taught in freshmen and sophomore year by presenting several areas of recent development and application. In this team-taught seminar-style course, two or three different professors will introduce students to their research areas and related topics. Some of the areas represented among the faculty include fractal geometry, number theory, algebraic geometry, and probability. Students will also be introduced to resources provided by national mathematical communities on mathematical career paths and backgrounds needed.

#### MATH-255 Probability and Statistics

Prerequisites:

MATH-165 or MATH-164 with a grade of C or better

Credits:

4

Description:

Topics include: random variable and distribution; expectation and variance; special discrete/continuous distributions (uniform, binomial, negative binomial, geometric, hypergeometric, Poisson, normal, and exponential distributions); joint distribution, marginal distribution and conditional distribution; covariance; limit theorems (law of large numbers and central limit theorem); introduction to confidence interval and hypothesis testing; regression analysis. Offered as needed.

#### MATH-265 Calculus III

Prerequisites:

MATH 166 with grade of C or better

Credits:

4

Description:

Parametric equations and polar coordinates (curves, areas, conic sections); vectors and the geometry of space (the dot product, vector arithmetic, lines and planes in 3-space, the cross product, cylinders and quadratic surfaces); vector functions (limits, derivatives and integrals, motion in space); partial derivatives (functions of several variables, limits and continuity, tangent planes and differentials, chain rule, directional derivatives, gradient, extrema, Lagrange multipliers); multiple integrals (double integrals, applications); vector calculus (vector fields, line integrals, fundamental theorem for line integrals, Green's Theorem, curl and divergence, parametric surfaces, surface integrals). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.

#### MATH-285 Discrete Mathematics II

Prerequisites:

Take MATH-185 with a grade of C or better

Credits:

4

Description:

Topics covered include: Algorithms, growth of functions (big O notation), computational complexity of algorithms, divide-and-conquer algorithms, graphs and their properties (isomorphisms of graphs, Euler and Hamilton paths, shortest path problem, graph coloring) trees (tree traversal, minimum spanning trees). As time allows: matrices and linear transformations.

#### MATH-290 Financial Mathematics I

Prerequisites:

MATH-166, 164 or 165 with a minimum grade of C

Credits:

4

Description:

This course is mainly designed for students who are interested in financial mathematics and/or actuarial sciences, especially if they plan to take the second actuarial exam, and/or if they plan to study more in financial mathematics. The materials covered include time value of money, annuities, loans, bonds, cash flows and portfolios, general derivatives, options, hedging and investment strategies, forwards and futures, and swaps.

#### MATH-331 Introduction to Advanced Mathematics

Prerequisites:

Take MATH-185 with a grade of C or better

Credits:

4

Description:

this course is intended to provide a firm foundation for and a taste of the study of advanced mathematics. While the course content varies somewhat, it is designed to give students a deeper understanding of the algebraic and analytical structure of the integers, the rational numbers and the real numbers and how they act as a building block to a variety of fields of mathematics. Students are introduced to the process of mathematical discovery and the language of mathematics. Exercises and projects are designed to illustrate the need for proof and to further refine the student's ability to analyze, conjecture and write mathematical proofs. This course is a prerequisite for most upper level mathematics courses and, after completing it a student will be in a position to determine realistically if he or she ought to major or minor in mathematics.

#### MATH-357 Math Statistical Analysis

Prerequisites:

MATH-255 with a minimum C grade

Credits:

4

Description:

Calculus based introduction to statistical analysis. Topics include sampling distribution, point estimation, interval estimation, hypothesis testing, regression and correlation analysis.

#### MATH-373 Ordinary Differential Equations

Prerequisites:

MATH-265 (may be taken concurrently)

Credits:

4

Description:

A first course in differential equations. Topics generally include separable, homogeneous, exact, and linear first order differential equations; variations of parameters, differential operators, the Laplace transform, inverse transforms, systems of differential equations, power series solutions, Fourier series, and applications.

#### MATH-431 Linear Algebra

Prerequisites:

Math 331 must have grade C or higher

Credits:

4

Description:

System of linear equations, Gaussian elimination, matrices and their algebra, inverse of a matrix, determinants, cofactor expansion, Cramer's rule, vectors in and their algebra, abstract vector spaces, subspaces, linear independence, basis and dimension, linear transformations, isomorphism of vector spaces, rank and nullity, matrix of a linear transformation, inner product spaces, angle and orthogonality, eigenvalues and eigenvectors of a linear transformation, characteristic equation, Cayley-Hamilton theorem, diagonalization.

#### MATH-432 Abstract Algebra

Prerequisites:

MATH 431

Credits:

4

Description:

An introduction to elementary group theory, including properties of groups, subgroups, first isomorphism theorem for groups, normal subgroups, finite group classification; elementary properties of rings, such as homomorphisms of rings, ideals, fields, Euclidean algorithm, rings of polynomials, factorization theory, integral domains, associates, primes and units in domains, and other topics in number theory. Prerequisite: MATH 431 with a grade of C or higher.

#### MATH-462 Real Analysis

Prerequisites:

MATH 331 with at least a grade of C

Credits:

4

Description:

A detailed treatment of the basic concepts of analysis including the real numbers; completeness and its equivalence to other properties of the reals such as monotone convergence, Archimedean property, Bolzano-Weierstrass theorem; the topology of Euclidean spaces, compactness and the Heine-Borel theorem, connectedness, continuity and uniform continuity and uniform continuity, pointwise and uniform convergence of functions, and an introduction to metric spaces.

#### MATH-481 Complex Analysis I

Prerequisites:

MATH-331

Credits:

4

Description:

Construction and properties of complex numbers, calculus in the complex plane, analytic functions, contour integrals and the basics of Cauchy theory, power series representations. Prerequisite: MATH 331 or instructor's consent.

#### MATH-H500 Honors Senior Project in Mathematics

Prerequisites:

Instructor consent required

Credits:

1.00- 4.00

Description:

Students study an advanced mathematics topic in depth. Work typically results in a project of significant depth and breadth.

#### MATH-510 Independent Study

Credits:

4

Description:

Members of the department will hold conference hours with students and will direct their readings and study of topics in mathematics which may be of interest to them. Prerequisite: Consent of instructor. 1 term - credits to be arranged.

#### MATH-511 Launching a Career in Mathematics

Prerequisites:

Junior or Senior standing

Credits:

1

Description:

This team-taught course is designed to explore career opportunities in Mathematics in depth. This course focuses on career search, the application process, entry, transition and networking for career success. Alternative options such as graduate school will also be explored. Students articulate and reflect on academic work, and co-curricular experiences from the perspective of professionals entering or advancing their careers. The goal of this course is to help students reach their fullest professional potential following graduation.

#### MATH-512 Special Topic in Advanced Math

Prerequisites:

Instructor consent required

Credits:

1.00- 4.00

Description:

Students study a particular topic in advanced mathematics.

## Math Statistics Courses

#### STATS-240 Introduction to Statistics

Prerequisites:

Math 128 or higher. REMINDER: STATS 240 is a required prerequisite MKT 220, FIN 200 and ISOM 201(prerequisite for ISOM 319)

Credits:

4

Description:

Topics include: data presentation, measures of central locations and dispersion, probability and probability distributions, estimation, hypothesis testing, simple and multiple regression models. The use of Excel and SPSS will be emphasized throughout the course. 1 term - 4 credits (4 hours per week). Normally offered each semester. STATS 240 satisfies the same requirements as STATS 250

#### STATS-250 Applied Statistics

Prerequisites:

MATH 128 or higher. REMINDER: STATS 250 is a required prerequisite MKT 220, FIN 200 and ISOM 201(prerequisite for ISOM 319)

Credits:

4

Description:

Application of statistical analysis to real-world business and economic problems. Topics include data presentation, descriptive statistics including measures of location and dispersion, introduction to probability, discrete and continuous random variables, probability distributions including binomial and normal distributions, sampling and sampling distributions, statistical inference including estimation and hypothesis testing, simple and multiple regression analysis. The use of computers is emphasized throughout the course. Normally offered each semester.

#### STATS-H250 Honors Applied Statistics

Prerequisites:

MATH-128, MATH 130, 134, 146, 164 or 165 and Honors Course; GPA of 3.3 or higher

Credits:

4

Description:

Application of statistical analysis to real-world business and economic problems. Topics include data presentation, descriptive statistics including measures of location and dispersion, introduction to probability, discrete and continuous random variables, probability distributions including binomial and normal distributions, sampling and sampling distributions, statistical inference including estimation and hypothesis testing, simple and multiple regression analyses. The use of computers is emphasized throughout the course. Prerequisite: MATH 130, MATH 134, MATH 146, or MATH 165 Honors Course GPA of 3.2 or higher required. 1 term - 4 credits Normally offered every year.