- Faculty
- Field Description
- The Majors and CoursesMajor in Mathematics
- The Major in Actuarial Science
- The Major in Financial Mathematics
- The Minor and Courses
- Repeat for Mastery (Precalculus) and Calculus Prerequisite Changes IMPORTANT CHANGES for AY 2018-2019 and AY 2019-2020
- Courses in Mathematics (MTH)
- Department of Mathematics Web Site
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Field Description
Mathematics has been described as the queen of all sciences. Understanding mathematics enables one to explain and analyze not only science and nature but almost all disciplines from archeology to zoology. Most recently, mathematics has become an indispensable tool in finance and other business related areas. To ensure that mathematics is available for students with varied backgrounds and different professional goals, the department offers courses at all levels. Advanced courses are designed to be taken by mathematics and actuarial science majors and those in related fields.
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The Majors
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A student majoring in mathematics cannot declare a second major in statistics.
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Program Learning Goals
Upon completion of the two-year sequence in calculus, students will be able to:
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- Solve differential equations using series expansions, Laplace transforms, and other standard techniques [differential equations];
- Enunciate properties and applications of Eulerian, Hamiltonian, connected, cyclic, acyclic, planar, traversable, and other types of graphs [graph theory];
- Approach combinatorics problems from two points of view which, when united, lead to solutions of problems in combinatorics using permutations, combinations, partitions, mathematical induction [combinatorics];
- Trace the historical development of mathematics from antiquity to the present, including contributions to that cumulative subject from various cultures and countries [history of mathematics];
- Stipulate properties and characteristics of whole numbers – divisibility, the division algorithm, Diophantine equations, unique factorization, the integers modulo n, Fermat’s theorem, Euler’s theorem, representation in different bases [theory of numbers];
- Write computer programs in a high-level programming language to solve mathematical problems and verify their correctness, and invoke techniques of object-oriented programming to represent objects and their behaviors in code [algorithms, computers, and programming class].
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Major Course Requirements
Math Program Prerequisites | ||||||||||||||||||||
Option 1: | 8 credits | |||||||||||||||||||
Calculus AP Exam (BC) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||
And one of the following: | ||||||||||||||||||||
| Intermediate Calculus | 4 credits | ||||||||||||||||||
or | ||||||||||||||||||||
| Multi-Variable and Vector Calculus * | 4 credit | ||||||||||||||||||
or | ||||||||||||||||||||
Option 2: | 12 credits | |||||||||||||||||||
Calculus AP Exam (AB) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||
and | ||||||||||||||||||||
| Calculus I | 4 credits | ||||||||||||||||||
And one of the following: | ||||||||||||||||||||
| Intermediate Calculus | 4 credits | ||||||||||||||||||
or | ||||||||||||||||||||
| Multi-Variable and Vector Calculus * | 4 credits | ||||||||||||||||||
or | ||||||||||||||||||||
Option 3: | 12 credits | |||||||||||||||||||
| Calculus I | 4 credits | ||||||||||||||||||
and | ||||||||||||||||||||
| Calculus II | 4 credits | ||||||||||||||||||
And one of the following: | ||||||||||||||||||||
| Intermediate Calculus | 4 credits | ||||||||||||||||||
or | 4 credits | |||||||||||||||||||
| Multi-Variable and Vector Calculus * | |||||||||||||||||||
or | ||||||||||||||||||||
Option 4: | 12-13 credits | |||||||||||||||||||
| Applied Calculus | 3 credits | ||||||||||||||||||
or | ||||||||||||||||||||
| Applied Calculus and Matrix Applications | 4 credits | ||||||||||||||||||
And the following two courses: | ||||||||||||||||||||
| Integral Calculus | 4 credits | ||||||||||||||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||||||||||||||
or | ||||||||||||||||||||
Option 5: | 12-13 credits | |||||||||||||||||||
or
| Applied Calculus | 3 credits | ||||||||||||||||||
or | ||||||||||||||||||||
| Applied Calculus and Matrix Applications | 4 credits | ||||||||||||||||||
and | ||||||||||||||||||||
| Integral Calculus | 4 credits | ||||||||||||||||||
and | ||||||||||||||||||||
| Infinite Series | 1 credit | ||||||||||||||||||
And one of the following: | ||||||||||||||||||||
| Intermediate Calculus | 4 credits | ||||||||||||||||||
or | ||||||||||||||||||||
| Multi-Variable and Vector Calculus * | 4 credits | ||||||||||||||||||
or | ||||||||||||||||||||
Option 6: | 10 credits | |||||||||||||||||||
| Analytic Geometry and Calculus I | 5 credits | ||||||||||||||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||||||||||||||
* MTH 3050 is not open to students who completed MTH 3020, MTH 3030, MTH 3035, or their equivalent. | ||||||||||||||||||||
Required Courses All students must take the following three courses: | ||||||||||||||||||||
| Algorithms, Computers and Programming I | 3 credits | ||||||||||||||||||
| Mathematical Analysis I (formerly Advanced Calculus) | 3 credits | ||||||||||||||||||
| Linear Algebra and Matrix Methods | 3 credits | ||||||||||||||||||
Electives Students must complete at least 15 elective credits from the following group of courses: | ||||||||||||||||||||
| Bridge to Higher Mathematics | 3 credits | ||||||||||||||||||
| Proof Writing for Mathematical Analysis | 1 credit | ||||||||||||||||||
| Topology | 3 credits | ||||||||||||||||||
| Advanced Calculus II | 3 credits | ||||||||||||||||||
| Ordinary Differential Equations | 3 credits | ||||||||||||||||||
| Introduction to Probability ** | 4 credits | ||||||||||||||||||
| Numerical Methods for Differential Equations in Finance | 4 credits | ||||||||||||||||||
| Introduction to Stochastic Process | 4 credits | ||||||||||||||||||
| Mathematics of Data Analysis (formerly Mathematics of Statistics) | 4 credits | ||||||||||||||||||
| Computational Methods in Probability | 3 credits | ||||||||||||||||||
| Graph Theory | 3 credits | ||||||||||||||||||
| Mathematical Modeling * | 3 credits | ||||||||||||||||||
| Combinatorics | 3 credits | ||||||||||||||||||
| Theory of Numbers | 3 credits | ||||||||||||||||||
| Elements of Modern Algebra | 3 credits | ||||||||||||||||||
| Introduction to Modern Geometry | 3 credits | ||||||||||||||||||
| History of Mathematics | 3 credits | ||||||||||||||||||
| Differential Geometry * | 3 credits | ||||||||||||||||||
| Algorithms, Computers and Programming II | 3 credits | ||||||||||||||||||
| Methods of Numerical Analysis | 3 credits | ||||||||||||||||||
| Introduction to Mathematical Logic | 3 credits | ||||||||||||||||||
| Fundamental Algorithms | 3 credits | ||||||||||||||||||
| Actuarial Mathematics I | 4 credits | ||||||||||||||||||
| Actuarial Mathematics II | 4 credits | ||||||||||||||||||
| Mathematics of Inferential Statistics | 4 credits | ||||||||||||||||||
| Short-Term Insurance Mathematics | 4 credits | ||||||||||||||||||
| Short-Term Insurance Mathematics II | 4 credits | ||||||||||||||||||
| Introductory Financial Mathematics | 4 credits | ||||||||||||||||||
| Data Analysis and Simulation for Financial Engineers | 4 credits | ||||||||||||||||||
| Advanced Calculus III * | 3 credits | ||||||||||||||||||
| Theory of Functions of a Complex Variable | 3 credits | ||||||||||||||||||
| Theory of Functions of Real Variables* | 3 credits | ||||||||||||||||||
| Partial Differential Equations and Boundary Value Problems* | 4 credits | ||||||||||||||||||
| Stochastic Calculus for Finance | 4 credits | ||||||||||||||||||
* These courses are offered infrequently, subject to student demand. ** Students may use the combination of
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Program Learning Goals
Upon completion of the required core courses in actuarial mathematics, students will be able to:
- Examine and solve problems dealing with discrete and continuous probability distributions.
- Recognize when a specific probability distribution is applicable.
- Determine an appropriate distribution to model a specific scenario in a risk-management context.
- Compute equivalent interest and discount rates (both nominal and effective).
- Write an equation of value for a set of cash flows. Estimate effective compound yield rates for the set of cash flows using a simple interest approximation.
- Calculate present and future values for various types of annuities and perpetuities such as annuities-due, perpetuities-due, annuities-immediate, perpetuities-immediate, arithmetic or geometric annuities, and non-level annuities.
- Determine the payment amount for a loan with a specific repayment structure.
- Find the outstanding balance immediately after a payment on a loan.
- Calculate the amount of principal and amount of interest in a payment for an amortized loan.
- Perform an amortization on a coupon bond.
- Compute yield rates for a callable bond at each of the call dates.
- Calculate values, duration, and convexity for both zero-coupon bonds and coupon bonds.
- Use first-order approximation methods based on duration to estimate the change in present value of a portfolio based on changes in interest rates.
- Construct an investment portfolio to immunize a set of liability cash flows.
- Calculate minimal variance portfolios with and without constraints.
- Perform pricing and hedging of European and American type derivative securities in the context of one- and multi-period binomial models.
- Construct arguments based on the no-arbitrage principle, and devise arbitrage strategies when this principle is violated.
- Price European derivative securities in the context of the Black-Scholes model.
- Derive a put-call parity relation, and use it for pricing and hedging.
Upon completion of elective courses in actuarial mathematics, students will be able to:
- Find closed-form solutions to ordinary and partial differential equations derived from financial models.
- Derive the celebrated Black-Scholes formula by solving the Black-Scholes PDE.
- Compute values of European, American, and exotic options using finite difference numerical methods.
- Download options market data and use it as input for codes generating implied volatility surfaces.
- Describe and classify different kinds of short-term insurance coverage.
- Explain the role of rating factors and exposure in pricing short-term insurance.
- Create new families of distributions by applying the technique of multiplication by a constant, raising to a power, exponentiation, or mixing.
- Calculate various measures of tail weight and interpret the results to compare tail weights.
- Calculate risk measures, including Value at Risk and Tail Value at Risk, and explain their properties, uses, and limitations.
- Calculate premiums using the pure premium and loss ratio methods.
- Use Maximum Likelihood Estimation and Bayesian Estimation to estimate parameters for severity, frequency, and aggregate distributions for individual, grouped, truncated, or censored data.
- Use hypothesis tests (e.g., Chi-square goodness-of-fit, Kolmogorov-Smirnov, and likelihood ratio tests) and score-based approaches (e.g., the Schwarz-Bayesian Criterion, the Bayesian Information Criterion, and the Akaike Information Criterion) to perform model selection on a collection of data.
- Apply credibility models such as the Buhlmann and Buhlmann-Straub models, and explicate the relationship between these models and Bayesian models.
- Explain the concepts of random sampling, statistical inference and sampling distribution.
- State and use basic sampling distributions.
- Describe and apply the main methods of estimation including matching moments, percentile matching, and maximum likelihood.
- Describe and apply the main properties of estimators including bias, variance, mean squared error, consistency, efficiency, and UMVUE.
- Construct confidence intervals for unknown parameters, including the mean, differences of two means, variances, and proportions.
- Analyze data using basic statistical inference tools like confidence intervals and hypothesis testing for the population mean.
- Apply tools such as analysis of variance, tests of significance, residual analysis, model selection, and predication in both the simple and multiple regression models.
- Demonstrate proficiency in some basic programming skills in SAS and the time-series Forecasting interactive system. Perform time-series analysis using these tools.
- Identify patterns in data such as trend or seasonality. Incorporate these patterns into the time-series analysis of the data, and perform error analysis of the data.
- Explain K-means and hierarchical clustering, and interpret the results of a cluster analysis.
Common Objectives – Actuarial and Financial Mathematics
Upon completion of the required finance courses for the actuarial science and financial mathematics majors, students will be able to:
- Expound on the governance of corporations.
- Outline the operation of financial markets and institutions.
- Measure corporate performance.
- Analyze risk and return. Determine the opportunity cost of capital.
- Perform capital budgeting using various techniques.
- Compute the present and future values of investments with multiple cash flows.
- Describe the mechanisms that cause fluctuation of bond yields.
- Calculate internal rate of return.
- Perform and interpret scenario analysis for a proposed investment.
- Calculate financial break-even points.
- Determine relevant cash flows for a proposed project.
- Determine a firm’s overall cost of capital.
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Major Course Requirements
Math Program Prerequisites Based on placement, follow one of the following preliminary calculus options below: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 1: |
| 8 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Calculus AP Exam (BC) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: |
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| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Multi-Variable and Vector Calculus * | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 2: |
| 12 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Calculus AP Exam (AB) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
and |
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| Calculus II | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: |
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| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 1: |
| 8 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Calculus AP Exam (BC) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: |
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| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Multi-Variable and Vector Calculus * | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 2: |
| 12 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Calculus AP Exam (AB) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
and |
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| Calculus II | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: |
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| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Multi-Variable and Vector Calculus * | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 3: |
| 12 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Calculus I | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
and |
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| Calculus II | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Multi-Variable and Vector Calculus * | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 4: |
| 12-13 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Applied Calculus
| 3 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Applied Calculus and Matrix Applications | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And the following two courses: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Integral Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Analytic Geometry and Calculus II | 5 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 5: |
| 12-13 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or
| Applied Calculus
Applied Calculus and Matrix Applications | 3 credits
4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And |
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and
| Integral Calculus
Infinite Series | 4 credits
1 credit | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Plus one of the following: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Intermediate Calculus | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Multi-Variable and Vector Calculus * | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 6: |
| 10 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Analytic Geometry and Calculus I | 5 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Analytic Geometry and Calculus II | 5 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
NOTE: *
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Business Program Prerequisites | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Principles of Accounting | 3 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Multi-Variable and Vector Calculus Introduction to Business ** | 3 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 3: |
| 12 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| BUS | Business Fundamentals: The Contemporary Business Landscape ** | 3 credits |
| Calculus I | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
and |
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| Introduction to Information Systems and Technologies ** | 3 creditsCalculus II | 4 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And one of the following: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Micro-Economics | 3 credits |
| Intermediate Calculus | 4 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Macro-Economics | Multi-Variable and Vector Calculus * | 4 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 4: |
| 12-13 3 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Business Statistics I ** | 3 credits |
| Applied Calculus Principles of Finance | 3 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or |
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| Corporate Finance | 3 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Applied Calculus and Matrix Applications | 4 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
And the following two courses: NOTES: ** Students who have completed | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4120
| or both Integral Calculus | 4 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 3120
| Analytic Geometry and Calculus II | 5 credits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
or | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Option 5: |
| 12-13 credits | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4119
| , may have the following /
| 3000
| FIN
| prerequisites waived: or
| 1000
| BUS | /
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Applied Calculus
Applied Calculus and Matrix Applications
3 credits
4 credits
And
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and
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Integral Calculus
Infinite Series
4 credits
1 credit
Plus one of the following:Required Courses
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Algorithms, Computers, and Programming I
Intermediate Calculus
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Introduction to Probability ***Multi-Variable and Vector Calculus *
4 credits
or
Option 6:
10 credits
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Theory of Interest
4 credits
Analytic Geometry and Calculus I
5 credits
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Actuarial Mathematics I
4 credits
Analytic Geometry and Calculus II
5 credits
NOTE:
*
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Actuarial Mathematics II
is not open to students who completed
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Short-Term Mathematics
4 credits
,
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Short-Term Mathematics II
4 credits
,
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Introductory Financial Mathematics
4 credits
, or their equivalents.
Business Program Prerequisites*** Students who have completed
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Principles of Accounting
3 credits
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Introduction to Business **
3 credits
or
Electives
In addition, one course must be chosen from the following list of electives:Showcourse v | |
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Numerical Methods for Differential Equations in Finance
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Business Fundamentals: The Contemporary Business Landscape **
3 credits
4 credits
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Introduction to Stochastic ProcessesInformation Systems and Technologies **
3 4 credits
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Mathematics of Data Analysis (formerly Mathematics of Statistics)
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Micro-Economics
3 4 credits
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Macro-EconomicsComputational Methods in Probability
3 credits
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Actuarial Mathematics Business Statistics I **
4 3 credits
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Actuarial Mathematics II
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Principles of Finance
3 4 credits
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Mathematics of Inferential Statistics
4 credits
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Corporate Finance
3 credits
NOTES:
** Students who have completed
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Short-Term Mathematics
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Short-Term Mathematics II
4 credits
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Introductory Financial Mathematics
4 credits
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Data Analysis and Simulation for Financial Engineers
4 credits
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Stochastic Calculus for Finance
4 credits
The following courses are recommended, but not required. They are not applicable toward the major.
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Intermediate Micro-Economics
3 credits
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Intermediate Macro-Economics
3 credits
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Required Courses | ||||||||||||||||||||||||||||||||||||||||||
| Algorithms, Computers, and Programming I | 3 credits | ||||||||||||||||||||||||||||||||||||||||
| Introduction to Probability *** | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Theory of Interest | 4 credits | ||||||||||||||||||||||||||||||||||||||||
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Students must also complete three of the following five courses: | ||||||||||||||||||||||||||||||||||||||||||
| Actuarial Mathematics I | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Actuarial Mathematics II | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Short-Term Mathematics | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Short-Term Mathematics II | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Introductory Financial Mathematics | 4 credits | ||||||||||||||||||||||||||||||||||||||||
*** Students who have completed
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Electives In addition, one course must be chosen from the following list of electives: | ||||||||||||||||||||||||||||||||||||||||||
| Numerical Methods for Differential Equations in Finance | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Introduction to Stochastic Processes | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Mathematics of Data Analysis (formerly Mathematics of Statistics) | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Computational Methods in Probability | 3 credits | ||||||||||||||||||||||||||||||||||||||||
| Actuarial Mathematics I | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Actuarial Mathematics II | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Mathematics of Inferential Statistics | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Short-Term Mathematics | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Short-Term Mathematics II | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Introductory Financial Mathematics | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Data Analysis and Simulation for Financial Engineers | 4 credits | ||||||||||||||||||||||||||||||||||||||||
| Stochastic Calculus for Finance | 4 credits | ||||||||||||||||||||||||||||||||||||||||
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The following courses are recommended, but not required. They are not applicable toward the major. | ||||||||||||||||||||||||||||||||||||||||||
| Intermediate Micro-Economics | 3 credits | ||||||||||||||||||||||||||||||||||||||||
| Intermediate Macro-Economics | 3 credits |
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Financial Mathematics
This major is first and foremost a course of study in mathematics, with a focus on the computational tools and techniques needed to thrive in the financial engineering industry. In today’s specialized world, a sophisticated level of mathematical understanding is an essential competitive edge. As this program includes courses in Economics and Finance, students who would usually not consider a traditional mathematics major will find this program especially attractive. Interested students are urged to contact the Department of Mathematics as early as possible. The student will be assigned an advisor who will aid in formulating an appropriate course of study.
A student majoring in financial mathematics cannot minor in mathematics or declare a second major in statistics.
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Program Learning Goals
Upon completion of the major in Financial Mathematics, students will be able to:
- Perform linear algebraic calculations such as matrix multiplication and inversion, solving systems of linear equations, Gram-Schmidt orthogonalization, Cholesky decomposition, computation of eigenvalues and eigenvectors.
- Obtain exact and numerical solutions to differential equations arising in finance such as the Black-Scholes model and its corresponding partial differential equation.
- Compute implied asset price volatilities for European and American options from options market data.
- Compute empirical volatilities from asset price time series using GARCH-type models.
- Apply the fundamental notions of probability theory – including continuous and discrete random variables, expected value and variance, conditional expectation, multivariate distributions, the law of large numbers, the central limit theorem, and moment-generating functions – to settings in finance where randomness arises, such as in the modelling of asset prices and interest rates.
- Apply the basic properties of martingales.
- Calculate minimum variance portfolios in a Markowitz and CAPM setting.
- Calculate call and put stock option values using a binomial model.
- Calculate call and put option values using the Black-Scholes model.
- Compute expectation for random variables and probabilities of events pertaining to Brownian motion.
- Compute expectations of functions of Ito processes using the Ito formula.
- Apply stochastic calculus to financial situations.
- Apply the theory of Markov chains to appropriate settings. Examples include: the computation of invariant distributions, the implementation of the Hastings-Metropolis algorithm, and Gibbs sampling.
- Apply the theory of arrival processes to settings such as corporate default models.
- Apply the theory of Brownian motion and related continuous-time stochastic processes such as the Ornstein-Uhlenbeck process to model the evolution of correlated asset values over time as well as the evolution of the Treasury yield curve over time.
- Use tools of statistical inference in the context of financial data. These tools include Bayesian estimation, maximum likelihood estimation, multiple regression analysis, confidence intervals, the t- and F-distributions for determining statistical significance, and analysis of variance.
- Implement Black-Karasinski and Hull-White and related lattice-based interest rate models to value fixed-income derivative securities like options on bonds, interest rate swaps, caps, floors, and swaptions.
- Build simulative interest-rate models based on continuous-time stochastic processes to value fixed-income derivative securities.
- Build elementary computer programs in Python and C++ to simulate stochastic processes.
- Use these models to calculate a fixed-income security’s duration, convexity, and key-rate duration for hedging purposes.
Common Objectives – Actuarial and Financial Mathematics
Upon completion of the required finance courses for the actuarial science and financial mathematics majors, students will be able to:
- Expound on the governance of corporations.
- Outline the operation of financial markets and institutions.
- Measure corporate performance.
- Analyze risk and return. Determine the opportunity cost of capital.
- Perform capital budgeting using various techniques.
- Compute the present and future values of investments with multiple cash flows.
- Describe the mechanisms that cause fluctuation of bond yields.
- Calculate internal rate of return.
- Perform and interpret scenario analysis for a proposed investment.
- Calculate financial break-even points.
- Determine relevant cash flows for a proposed project.
- Determine a firm’s overall cost of capital.
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Major Course Requirements
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Financial Mathematics
This major is first and foremost a course of study in mathematics, with a focus on the computational tools and techniques needed to thrive in the financial engineering industry. In today’s specialized world, a sophisticated level of mathematical understanding is an essential competitive edge. As this program includes courses in Economics and Finance, students who would usually not consider a traditional mathematics major will find this program especially attractive. Interested students are urged to contact the Department of Mathematics as early as possible. The student will be assigned an advisor who will aid in formulating an appropriate course of study.
A student majoring in financial mathematics cannot minor in mathematics or declare a second major in statistics.
...
NOTE: Depending on a student's starting mathematics proficiency, this program may require more than 120 credits to complete. | ||||||||||||||
Mathematics Program Prerequisites: | ||||||||||||||
As a preliminary requirement, students must complete the calculus requirement, which may be achieved by any one of the following six methods: | ||||||||||||||
Option 1: | ||||||||||||||
Calculus AP Exam (BC) with a score of 4 or 5 (transfers to Baruch as
| 8 credits | |||||||||||||
| Multi-Variable and Vector Calculus | 4 credits | ||||||||||||
or | ||||||||||||||
Option 2: | ||||||||||||||
| Calculus AP exam (AB) with a score of 4 or 5 (transfers to Baruch as
| 4 credits | ||||||||||||
| Calculus II | 4 credits | ||||||||||||
| Multi-Variable and Vector Calculus | 4 credits | ||||||||||||
or | ||||||||||||||
Option 3: | ||||||||||||||
| Calculus I | 4 credits | ||||||||||||
| Calculus II | 4 credits | ||||||||||||
| Multi-Variable and Vector Calculus | 4 credits | ||||||||||||
or | ||||||||||||||
Option 4: | ||||||||||||||
| Applied Calculus | 3 credits | ||||||||||||
or | ||||||||||||||
| Applied Calculus and Matrix Applications | 4 credits | ||||||||||||
and the following three courses: | ||||||||||||||
| Integral Calculus | 4 credits | ||||||||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||||||||
| Vector Calculus * | 1 credit | ||||||||||||
or | ||||||||||||||
Option 5: | ||||||||||||||
| Applied Calculus | 3 credits | ||||||||||||
| Applied Calculus and Matrix Applications | 4 credits | ||||||||||||
and the following three courses: | ||||||||||||||
| Integral Calculus | 4 credits | ||||||||||||
| Infinite Series | 1 credit | ||||||||||||
| Multi-Variable and Vector Calculus * | 4 credits | ||||||||||||
or | ||||||||||||||
Option 6: | ||||||||||||||
| Analytic Geometry and Calculus I | 5 credits | ||||||||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||||||||
| Vector Calculus * | 1 credit | ||||||||||||
Each option also requires: | ||||||||||||||
| Bridge to Higher Mathematics | 4 credits | ||||||||||||
* NOTES:
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Business Program Prerequisites: | ||||||||||||||
| Principles of Accounting | 3 credits | ||||||||||||
| Micro-Economics | 3 credits | ||||||||||||
| Macro-Economics | 3 credits | ||||||||||||
BSFM students are not required to complete the following FIN 3000 course prerequisites: BUS 1000/1011; CIS 2200; and STA 2000. Please consult the Weissman Associate Dean's Office (WSAS.AssocDean@baruch.cuny.edu; 646-312-3890; VC 8-265) to request registration permission. | ||||||||||||||
Required Finance Courses: | ||||||||||||||
| Principles of Finance | 3 credits | ||||||||||||
| Corporate Finance | 3 credits | ||||||||||||
Required Upper-level Mathematics Courses: | ||||||||||||||
| Algorithms, Computers, and Programming I | 3 credits | ||||||||||||
| Linear Algebra | 3 credits | ||||||||||||
| Numerical Methods for Differential Equations | 4 credits | ||||||||||||
| Introduction to Probability * | 4 credits | ||||||||||||
| Introduction to Stochastic Processes | 4 credits | ||||||||||||
| Mathematics of Data Analysis (formerly Mathematics of Statistics) | 4 credits | ||||||||||||
| Algorithms, Computers, and Programming II | 3 credits | ||||||||||||
| Introductory Financial Mathematics | 4 credits | ||||||||||||
| Data Analysis and Simulation for Financial Engineers | 4 credits | ||||||||||||
| Stochastic Calculus for Finance | 3 credits |
* Students who have completed |
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The Minor
The minor in mathematics provides students with a background in the various theories and uses of mathematics. The minor requires the completion of MTH 3006, MTH 3010, MTH 3020, MTH 3030, or MTH 3050, and any other 3- or 4- or 5-credit mathematics course numbered 3000 or higher with the exception of
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This minor is not open to students who are pursuing a major in statistics.
Required Course All students must take one of the following courses: | ||||||||
| Integral Calculus | 4 credits | ||||||
| Calculus II | 4 credits | ||||||
| Intermediate Calculus | 4 credits | ||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||
| Multi-variable and Vector Calculus | 4 credits | ||||||
Electives Students must take any two other courses from the following list, with at least one of the courses being a 4000-level or higher capstone course: | ||||||||
| Intermediate Calculus | 4 credits | ||||||
| Analytic Geometry and Calculus II | 5 credits | ||||||
| Multi-variable and Vector Calculus | 4 credits | ||||||
| Elementary Probability | 3 credits | ||||||
| Algorithms, Computers and Programming I | 3 credits | ||||||
| Bridge to Higher Mathematics | 3 credits | ||||||
| Mathematical Analysis I (formerly Advanced Calculus) | 3 credits | ||||||
| Advanced Calculus II | 3 credits | ||||||
| Topology | 3 credits | ||||||
| Linear Algebra and Matrix Methods | 3 credits | ||||||
| Ordinary Differential Equations | 3 credits | ||||||
| Numerical Methods for Differential Equations in Finance | 4 credit | ||||||
| Introduction to Probability | 4 credits | ||||||
| Introduction to Stochastic Process | 4 credits | ||||||
| Mathematics of Data Analysis (formerly Mathematics of Statistics) | 4 credits | ||||||
| Computational Methods in Probability | 3 credits | ||||||
| Graph Theory | 3 credits | ||||||
| Mathematical Modeling * | 3 credits | ||||||
| Combinatorics | 3 credits | ||||||
| Theory of Numbers | 3 credits | ||||||
| Elements of Modern Algebra | 3 credits | ||||||
| Introduction to Modern Geometry | 3 credits | ||||||
| History of Mathematics | 3 credits | ||||||
| Differential Geometry * | 3 credits | ||||||
| Algorithms, Computers and Programming II | 3 credits | ||||||
| Methods of Numerical Analysis | 3 credits | ||||||
| Introduction to Mathematical Logic | 3 credits | ||||||
| Fundamental Algorithms | 3 credits | ||||||
| Actuarial Mathematics I | 4 credits | ||||||
| Actuarial Mathematics II | 4 credits | ||||||
| Mathematics of Inferential Statistics | 4 credits | ||||||
| Short-Term Insurance Mathematics | 4 credits | ||||||
| Short-Term Insurance Mathematics II | 4 credits | ||||||
| Introductory Financial Mathematics | 4 credits | ||||||
| Data Analysis and Simulation for Financial Engineers | 4 credits | ||||||
| Advanced Calculus III * | 3 credits | ||||||
| Theory of Functions of a Complex Variable | 3 credits | ||||||
| Theory of Functions of Real Variables* | 3 credits | ||||||
| Partial Differential Equations and Boundary Value Problems* | 4 credits | ||||||
| Stochastic Calculus for Finance | 4 credits | ||||||
* These courses are offered infrequently, subject to student demand. |
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Repeat for Mastery (Precalculus) and Calculus Prerequisite Changes
This pilot program, which consists of two parts, will run as an experiment for academic years 2018-2019 and 2019-2020.
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Courses in Mathematics (MTH)
| Intermediate and College Algebra | 4.5 hours; 2 credits | ||||||
| College Algebra | 4 hours; 2 credits | ||||||
| Pre-calculus and Elements of Calculus | 4 hours; 3 credits | ||||||
| Precalculus | 4.5 hours; 3 credits | ||||||
| Mathematics Appreciation | 3 hours; 3 credits | ||||||
| Mathematics and Quantitative Reasoning | 4 hours; 3 credits | ||||||
| Ideas in Mathematics and Their Applications | 4 hours; 3 credits | ||||||
| Applied Calculus | 4 hours; 3 credits | ||||||
| Applied Calculus | 3 hours; 3 credits | ||||||
| Applied Calculus and Matrix Applications | 4 hours; 4 credits | ||||||
| Concepts of Discrete Mathematics | 3 hours; 3 credits | ||||||
| Calculus I | 4 hours; 4 credits | ||||||
| Analytic Geometry and Calculus I | 5 hours; 5 credits | ||||||
| Integral Calculus | 4 hours; 4 credits | ||||||
| Infinite Series | 1 hour; 1 credit | ||||||
| Elementary Calculus II | 4 hours; 4 credits | ||||||
| Intermediate Calculus | 4 hours; 4 credits | ||||||
| Analytic Geometry and Calculus II | 5 hours; 5 credits | ||||||
| Vector Calculus | 1 hour; 1 credit | ||||||
| Actuarial Seminar: R for Actuaries | 2 hours; 2 credits | ||||||
| Multi-Variable and Vector Calculus | 4 hours; 4 credits | ||||||
| Selected Topics in Discrete Mathematics | 3 hours; 3 credits | ||||||
| Elementary Probability | 3 hours; 3 credits | ||||||
| Algorithms, Computers, and Programming I | 4 hours; 3 credits | ||||||
| Actuarial Science Internship | 1 hour; 1 credit | ||||||
| Actuarial Science Internship | 1 hour; 1 credit | ||||||
| Actuarial Science Internship | 1 hour; 1 credit | ||||||
| Actuarial Science Internship | 1 hour; 1 credit | ||||||
| Math Internship | 1 hour; 1 credit | ||||||
| Math Internship | 1 hour; 1 credit | ||||||
| Math Internship | 1 hour; 1 credit | ||||||
| Math Internship | 1 hour; 1 credit | ||||||
| Financial Mathematics Internship | 1 hour; 1credit | ||||||
| Financial Mathematics Internship | 1 hour; 1credit | ||||||
| Financial Mathematics Internship | 1 hour; 1credit | ||||||
| Financial Mathematics Internship | 1 hour; 1credit | ||||||
| Bridge to Higher Mathematics | 4 hours; 3 credits | ||||||
| Problem-Solving Seminar | 3 hours; 3 credits | ||||||
| Proof Writing for Mathematical Analysis (formerly Proof Writing for Advanced Calculus) | 1 hour; 1 credit | ||||||
| Mathematical Analysis I | 3 hours; 3 credits | ||||||
| Advanced Calculus II | 3 hours; 3 credits | ||||||
| Topology | 3 hours; 3 credits | ||||||
| Linear Algebra and Matrix Methods | 3 hours; 3 credits | ||||||
| Ordinary Differential Equations | 3 hours; 3 credits | ||||||
| Numerical Methods for Differential Equations in Finance | 4 hours; 4 credits | ||||||
| Multivariate Probability Distributions | 1 hour; 1 credit | ||||||
| Introduction to Probability | 4 hours; 4 credits | ||||||
| Introduction to Stochastic Processes | 4 hours; 4 credits | ||||||
| Mathematics of Data Analysis (formerly Mathematics of Statistics) | 4 hours; 4 credits | ||||||
| Computational Methods in Probability | 4 hours; 3 credits | ||||||
| Graph Theory | 3 hours; 3 credits | ||||||
| Mathematical Modeling | 3 hours; 3 credits | ||||||
| Combinatorics | 3 hours; 3 credits | ||||||
| Theory of Numbers | 3 hours; 3 credits | ||||||
| Elements of Modern Algebra | 3 hours; 3 credits | ||||||
| Finite Fields, Algebraic Curves, and Applications | 3 hours; 3 credits | ||||||
| History of Mathematics | 4 hours; 4 credits | ||||||
| Differential Geometry | 3 hours; 3 credits | ||||||
| Algorithms, Computers, and Programming II | 4 hours; 3 credits | ||||||
| Methods of Numerical Analysis | 3 hours; 3 credits | ||||||
| Introduction to Mathematical Logic | 4 hours; 3 credits | ||||||
| Fundamental Algorithms | 4 hours; 3 credits | ||||||
| Switching Theory | 3 hours; 3 credits | ||||||
| Special Topics in Computer Science | 3 hours; 3 credits | ||||||
| Finite Differences | 4 hours; 4 credits | ||||||
| Theory of Interest | 4 hours; 4 credits | ||||||
| Actuarial Mathematics I | 4 hours; 4 credits | ||||||
| Actuarial Mathematics II | 4 hours; 4 credits | ||||||
| Mathematics of Inferential Statistics | 4 hours; 4 credits | ||||||
| Short-Term Insurance Mathematics (formerly Risk Theory) | 4 hours; 4 credits | ||||||
| Short-Term Insurance Mathematics II | 4 hours; 4 credits | ||||||
| Introductory Financial Mathematics | 4 hours; 4 credits | ||||||
| Data Analysis and Simulation for Financial Engineers | 4 hours; 4 credits | ||||||
| Independent Study I | Hours and credits to be arranged | ||||||
| Independent Study II | Hours and credits to be arranged | ||||||
| Independent Study III | Hours and credits to be arranged | ||||||
| Independent Study IV | Hours and credits to be arranged | ||||||
| Independent Study V | Hours and credits to be arranged | ||||||
| Advanced Calculus III | 3 hours; 3 credits | ||||||
| Theory of Functions of a Complex Variable | 3 hours; 3 credits | ||||||
| Theory of Functional of Real Variables | 3 hours; 3 credits | ||||||
| Partial Differential Equations and Boundary Value Problems | 4 hours; 4 credits | ||||||
| Stochastic Calculus for Finance | 4 hours; 4 credits | ||||||
| Honors in Mathematics I | Hours and credits to be arranged | ||||||
| Honors in Mathematics II | Hours and credits to be arranged | ||||||
| Honors in Mathematics III | Hours and credits to be arranged |
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