2021-2022 Undergraduate Bulletin

Applied Mathematics: Data Science and Cryptography, Bachelor of Science

The Applied Mathematics major has two concentrations, Data Science and Cryptography. The Data Science concentration presents the principles of data representation, big data management, and statistical modeling. Students learn to use modern computing techniques to reveal hidden causal and temporal relationships within large data sets. Hidden information is often benign but it might also be evidence of malevolent activities that have already occurred or are in progress. Cryptography is the science of both personal and institutional data security. Students learn to secure information, maintain data integrity, authenticity, and non-reputability. Cryptologists play a vital role in detecting events yet to unfold, especially when attempting to interdict and thwart incipient cyber intrusions and terrorist attacks.

The curriculum offers an integrated academic program with the depth and breadth necessary to make graduates truly competitive in the job market. Both concentrations provide the knowledge and the skills that are in demand in high tech entrepreneurship, finance, modern communications, medicine, security, transportation, and manufacturing. The New York City metropolitan region is being repositioned as a nexus of technological innovation and discovery as well as a haven for entrepreneurial leadership. Such a metamorphosis requires the availability of a renewable work force possessing skills in data analysis and data security. Consequently, employment opportunities are expected to be available for applied mathematics graduates for the foreseeable future.

Those individuals that opt to undertake graduate study will find that they are well prepared to enroll in a wide range of Masters and Doctoral programs such as Digital Forensics and Cyber Security, Financial Mathematics, Machine Learning, traditional Mathematics, and Mathematics Education. Indeed, the required mathematics core aligns well with the core requirements of other CUNY mathematics programs thereby affording graduates the widest possible choice of subsequent educational opportunities.

Learning Outcomes. Students will:

  • Apply the principles of mathematical proof and deductive logic to prove level appropriate mathematical statements or create counterexamples within the context of the real number axioms and the axioms defining various algebraic structures.
  • Apply the mathematical modeling process to modern problems in data science and cryptography for the purpose of analyzing large data sets and encrypting plain text or decrypting cipher text.
  • Function effectively in an interdisciplinary team environment and express quantitative information effectively to others.
  • Identify and adhere to the ethical constraints of respecting personal data privacy and evaluate and assess ethical standards for the application of cryptographic algorithms in contemporary contexts. 

Credits Required.

Applied Mathematics: Data Science & Cryptography Major   
51-57
General Education 42
Electives 21-27
Total Credits Required for B.S. Degree 120

Coordinator.
Professor Samuel Graff, Department of Mathematics and Computer Science (212-237-8767, sgraff@jjay.cuny.edu)  

Advisors. Professors Hunter Johnson (212.237.8846, hujohnson@jjay.cuny.edu), Shaobai Kan (646.557.4866, skan@jjay.cuny.edu), Michael Puls (212.484.1178, mpuls@jjay.cuny.edu),  Antoinette Trembinska (212.237.8838, atrembinska@jjay.cuny.edu),  Department of Mathematics and Computer Science

Advising information. Applied Mathematics Advising Resources Page (including a Sample Four Year Advising Plan)

Additional information. Students who enrolled for the first time at the College or changed to this major in September 2021 or thereafter must complete the major in the form presented here. Students who enrolled prior to that date may choose the form shown here or the earlier version of the major. A copy of the earlier version may be obtained in the 2020-2021 Undergraduate Bulletin.

Foundational Courses

May be required depending on mathematics placement
MAT 141Pre-Calculus

3

Advisor recommendation: MAT 141 fulfills the Required Core: Mathematics and Quantitative Reasoning area of the Gen Ed Program.

Total Credit Hours: 0-3

Part One. Core Courses

Required
CSCI 271Introduction to Computer Science

3

CSCI 272Object-Oriented Programming

3

MAT 151Calculus I

4

OR

MAT 241Calculus I

3

MAT 152Calculus II

4

OR

MAT 242Calculus II

3

MAT 151 Calculus I (4 credits) is part of the new calculus sequence and was formerly MAT 241 Calculus I (3 credits).

MAT 152 Calculus II (4 credits) is part of the new calculus sequence and was formerly MAT 242 Calculus II (3 credits).

Part Two. Mathematics Core Courses

Required
MAT 253Calculus III

4

OR

MAT 243Calculus III

3

MAT 244Calculus IV

3

MAT 250Elements of Mathematical Proof

MAT 301Probability & Mathematical Statistics I

3

MAT 310Linear Algebra

3

MAT 351Introduction to Ordinary Differential Equations

3

CSCI 373Advanced Data Structures

3

MAT 253 Calculus III (4 credits) is part of the new calculus sequence and was formerly MAT 243 Calculus III (3 credits).

Part Three. Concentrations

Students must choose one concentration and complete four courses

Concentration A. Data Science

Data Science plays a critical role in analyzing large data sets which may have valuable information that is obscured by the sheer volume of the data itself. In the Data Science concentration, students will learn the principles of data representation, big data management, and statistical modeling. They will also be able to use computers to reveal hidden causal and temporal relationships in large data sets.

Learning outcomes for Data Science Concentration.
Student will:
  • Use mathematical methods to analyze and recognize the properties of large data sets as well as any anomalies.
  • Use suitable models such as linear regression, logical regression, to analyze data and predict probability distributions.
  • Recognize clustering in large data sets and explain its significance.

Required

CSCI 362Databases and Data Mining

3

MAT 302Probability and Mathematical Statistics II

3

MAT 367Multivariate Analysis

3

MAT 455Data Analysis

3

Concentration B. Cryptography

Cryptography is the science of data security, both personal and institutional, and as such is also an important component of justice. In the Cryptography concentration, students will learn to secure information which is achieved by assuring privacy as well as other properties of a communication channel, such as data integrity, authenticity, and non-reputability, depending upon the application. They will devise systems for companies to resist the unwarranted intrusions of hackers, to protect internal company and consumer data, and to act as consultants to research staff concerning the implementation of cryptographic and mathematical methods.

Learning outcomes for the Cryptography Concentration.
Students will:
  • Use the mathematics upon which specific cryptographic algorithms are based to analyze the strengths and weaknesses of cryptographic schemes.
  • Guarantee authenticity and integrity of data and ensure that transactions are non-repudiable, when appropriate.
  • Develop cryptographic algorithms.

Required
CSCI 360Cryptography and Cryptanalysis

3

MAT 341Advanced Calculus 1

3

MAT 410Abstract Algebra

3

MAT 460Mathematical Cryptography

3

Total Credit Hours: 12

Part Four. Electives

Choose two

MAT 323Operations Research Models I

3

MAT 324Operations Research Models II

3

MAT 352Applied Differential Equations

3

MAT 354Regression Analysis

3

MAT 365The Mathematics of Signal Processing

3

MAT 371Numerical Analysis

3

MAT 380Selected Topics in Mathematics

3

MAT 385Faculty Mentored Research Experience in Mathematics

3

MAT 442Advanced Calculus II

3

CSCI 358Machine Learning

3

CSCI 385Faculty Mentored Research Experience in Computer Science

3

CSCI 421Quantum Computing

3

ENG 253Technical Writing in Computer Science, Math, and Science

3

Total Credit Hours: 6

Total Credit Hours: 51-57