# Mathematics Summer Courses

*Classes listed as "online" during Session I or II will meet synchronously online during a portion of their scheduled meeting times with additional coursework to be completed asynchronously. Session III online courses are all asynchronous (exceptions are noted in course descriptions).
Hybrid courses will meet in person on campus; however, the university will continue to implement the Flexible Hybrid Learning Environment to keep the community safe and allow for the possibility of remote attendance as necessary.*

**Fordham students**please check courses in my.fordham.edu for the most accurate Attribute listings.**MATH 1000 R21 - Precalculus**

*Session II, July 6 - August 5, 2021
Online: TWTh, 9 a.m.-Noon*

This course does not fulfill the Mathematics reasoning portion of the Curriculum. The course is designed to allow students entry into calculus courses.

*CRN: 12666*

*Instructor: Brakalova
3 credits*

**MATH 1100 L11 - Finite Mathematics**

*Session I, June 1 - July 1, 2021
Online: TWTh, 1-4 p.m.*

Solutions to systems of linear equations, counting techniques including Venn diagrams, permutations, combinations, probability, Bayes theorem, Markov chains. This course is designed to introduce general liberal arts students to the use of mathematics as a tool in the solution of problems that arise in the "real world". Applications will be chosen from areas such as business, economics, and other social and natural sciences. These applications will be based upon mathematical topics chosen from a field called Finite Mathematics. Specific topics to be covered may include Linear Programming, Probability, Statistics, and Finance. The only prior knowledge expected is arithmetic, elementary algebra, and graphing, which students should already be familiar with from previous high school or college courses and/or the Mathematics Workshop. It will be presumed that students possess basic skills in these areas.

*CRN: 12484*

*Instructor: Ye
3 credits*

**MATH 1100 L12 - Finite Mathematics**

*Session I, June 1 - July 1, 2021
Online: TWTh, 9 a.m.-Noon*

Solutions to systems of linear equations, counting techniques including Venn diagrams, permutations, combinations, probability, Bayes theorem, Markov chains. This course is designed to introduce general liberal arts students to the use of mathematics as a tool in the solution of problems that arise in the "real world". Applications will be chosen from areas such as business, economics, and other social and natural sciences. These applications will be based upon mathematical topics chosen from a field called Finite Mathematics. Specific topics to be covered may include Linear Programming, Probability, Statistics, and Finance. The only prior knowledge expected is arithmetic, elementary algebra, and graphing, which students should already be familiar with from previous high school or college courses and/or the Mathematics Workshop. It will be presumed that students possess basic skills in these areas.

*CRN: 12495*

*Instructor: Adamski
3 credits*

**MATH 1100 L21 - Finite Mathematics**

*Session II, July 6 - August 5, 2021
Online: TWTh, 6-9 p.m.*

Solutions to systems of linear equations, counting techniques including Venn diagrams, permutations, combinations, probability, Bayes theorem, Markov chains. This course is designed to introduce general liberal arts students to the use of mathematics as a tool in the solution of problems that arise in the "real world". Applications will be chosen from areas such as business, economics, and other social and natural sciences. These applications will be based upon mathematical topics chosen from a field called Finite Mathematics. Specific topics to be covered may include Linear Programming, Probability, Statistics, and Finance. The only prior knowledge expected is arithmetic, elementary algebra, and graphing, which students should already be familiar with from previous high school or college courses and/or the Mathematics Workshop. It will be presumed that students possess basic skills in these areas.

*CRN: 12678*

*Instructor: Rotundo
3 credits*

**MATH 1108 R11 - Math For Business: Finite**

*Session I, June 1 - July 1, 2021
Online: TWTh, 9 a.m.-Noon*

Solutions to systems of linear equations, elementary matrix theory, linear programming, elementary counting techniques, probability, mathematics of finance.

*Closed*

*Instructor: Ye
3 credits*

**MATH 1109 L11 - Math For Business: Calculus**

*Session I, June 1 - July 1, 2021
Online: TWTh, 9 a.m.-Noon*

Calculus for business majors. Topics include derivatives of polynomial, rational, exponential and logarithm functions. Curve sketching and optimization problems. The definite integral. Applications are drawn from business and economics.

*Closed*

*Instructor: Wood
3 credits*

**MATH 1109 R11 - Math For Business: Calculus**

*Session I, June 1 - July 1, 2021
Online: TWTh, 6-9 p.m.*

Calculus for business majors. Topics include derivatives of polynomial, rational, exponential and logarithm functions. Curve sketching and optimization problems. The definite integral. Applications are drawn from business and economics.

*Closed*

*Instructor: Gindes
3 credits*

**MATH 1109 R21 - Math For Business: Calculus**

*Session II, July 6 - August 5, 2021
Rose Hill, Hybrid: TWTh, 9 a.m.-Noon*

Calculus for business majors. Topics include derivatives of polynomial, rational, exponential and logarithm functions. Curve sketching and optimization problems. The definite integral. Applications are drawn from business and economics.

*CRN: *12667

*Instructor: Martynovsky
3 credits*

**MATH 1203 R11 - Applied Calculus I**

*Session I, June 1 - July 1, 2021
Rose Hill, Hybrid: TWTh, 9 a.m.-Noon*

This course is designed for students who do not intend to take Calculus 2 or other upper-level math courses. Topics include derivatives of polynomial, rational, exponential, and logarithmic functions; curve sketching; and optimization problems.

*CRN: 12703*

*Instructor: Mast
3 credits*

**MATH 1203 PW1 - Applied Calculus**

*Session III, June 1 - August 5, 2021
Online, Asynchronous*

This course is designed for students who do not intend to take Calculus 2 or other upper-level math courses. Topics include derivatives of polynomial, rational, exponential, and logarithmic functions; curve sketching; and optimization problems.

*Closed*

*Instructor: Wisnewski
3 credits*

**MATH 1203 R22 - Applied Calculus I**

*Session II, July 6 - August 5, 2021
Online: TWTh, 9 a.m.-Noon*

This course is designed for students who do not intend to take Calculus 2 or other upper-level math courses. Topics include derivatives of polynomial, rational, exponential, and logarithmic functions; curve sketching; and optimization problems.

*CRN: 12670*

*Instructor: Alberge
3 credits*

**MATH 1206 L11 - Calculus I**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 6-9 p.m.*

Functions, limits, continuity, Intermediate Value Theorem. The derivative and applications, antiderivatives, Riemann sums, definite integrals, the Fundamental Theorem of Calculus.

*CRN: 12488*

*Instructor: Smith
4 credits*

**MATH 1206 R11 - Calculus I**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 1-4 p.m.*

Functions, limits, continuity, Intermediate Value Theorem. The derivative and applications, antiderivatives, Riemann sums, definite integrals, the Fundamental Theorem of Calculus.

*CRN: 12489*

*Instructor: Poor
4 credits*

**MATH 1206 L21 - Calculus I**

*Session II, July 6 - August 5, 2021
Online: MTWTh, 6-9 p.m.*

Calculus for science and math majors. Functions, limits, continuity, Intermediate Value Theorem. The derivative and applications, antiderivatives, Riemann sums, definite integrals, the Fundamental Theorem of Calculus.

*CRN: 12671*

*Instructor: Gu
4 credits*

**MATH 1207 R11 - Calculus II**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 6-9 p.m.*

A continuation of MATH 1206. The definite integral, area, volumes, work. Logarithm, inverse functions, techniques of integration, Taylor polynomials.

*CRN: 12490*

*Instructor: Boninger
4 credits*

**MATH 1207 R21 - Calculus II**

*Session II, July 6 - August 5, 2021
Online: MTWTh, 6-9 p.m.*

A continuation of MATH 1206. The definite integral, area, volumes, work. Logarithm, inverse functions, techniques of integration, Taylor polynomials.

*CRN: 12673*

*Instructor: Roy
4 credits*

**MATH 2001 L11 - Discrete Mathematics**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 9 a.m.-Noon*

This course introduces students to higher order mathematical thinking in the context of writing proofs using discrete structures. Topics include elementary logic; basic proof techniques such as direct proof, proof by contradiction, case division, contraposition, induction; division, Euclid’s algorithm, modular arithmetic; set theory, relations and functions; and equivalence. Additional topics may include cardinality of sets, combinatorics, and graphs.

*Closed*

*Instructor: Fu
4 credits*

**MATH 2004 R11 - Multivariable Calculus I**

*Session I, June 1 - July 1, 2021
Rose Hill, Hybrid: MTWTh, 9 a.m.-Noon*

The calculus of sequences and series, power series, uniform convergence, vector methods of solid geometry, vector valued functions, functions of several variables, partial derivatives, gradients, Lagrange multipliers.

*CRN: 12706*

*Instructor: Ryham
4 credits*

**MATH 2005 R21 - Multivariable Calculus II**

*Session II, July 6 - August 5, 2021
Online: MTWTh, 1-4 p.m.*

This is a continuation of MATH 2004. Topics include vector fields and their derivatives, multiple integrals, line and surface integrals, and the theorems of Gauss, Green and Stokes. Additional topics, as time permits, may cover one or more of the following: differential forms, functions of a complex variable, equations of fluid mechanics, or mean and Gauss curvature.

*CRN: 12674*

*Instructor: Gong
4 credits*

**MATH 2006 R11 - Linear Algebra**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 1-4 p.m.*

Topics include systems of linear equations, Real and complex vector spaces, linear independence, dimension, linear transformations, matrix representations, kernel and range, determinants, and eigenvalues.

*Closed*

*Instructor: Zappa
4 credits*

**MATH 3002 R21 - Differential Equations**

*Session II, July 6 - August 5, 2021
Rose Hill, Hybrid: MTWTh, 6-9 p.m.*

Topics covered in this course include existence and uniqueness theorems for ordinary differential equations, linear differential equations, power series solutions, Laplace transform, and numerical methods.

*CRN: 12675*

*Instructor: Ryham
4 credits*

**MATH 3005 L11 - Abstract Algebra**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 6-9 p.m.*

Topics include well-ordering and induction, unique factorization, modular arithmetic, groups, subgroups, Lagrange's theorem, normality, homomorphisms of groups, permutation groups, simple groups.

*CRN: 12493*

*Instructor: McFaddin
4 credits*

**MATH 3006 R11 - Probability**

*Session I, June 1 - July 1, 2021
Online: MTWTh, 6-9 p.m.*

Topics include discrete and continuous probability models in one and several variables, expectation, and variance, limit theorems, applications.

*CRN: 12494*

*Instructor: Golec
4 credits*