2016-2018 Undergraduate and Graduate Bulletin (with addenda) [ARCHIVED CATALOG]
Course Descriptions
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A Brief Guide to Course Descriptions
Each program described in this catalog contains detailed descriptions of the courses offered within the program.
The first line gives the official course number for which students must register and the official course title. The letters indicate the discipline of the course and the first number of the official course numbers indicates the level of the course. The levels are as follows:
- 1XXX - Freshman Level
- 2XXX - Sophomore Level
- 3XXX - Junior Level
- 4XXX - Senior Level
- 5XXX to 9XXX - Graduate level
Typically the last number of the course number indicates the number of credits. The breakdown of periods of the course is also listed.
When selecting a course for registration, the section of the course may include the following notations:
- “LEC” - lecture section
- “RCT” or “RC” - recitation section
- “LAB” or “LB” - lab section
Additionally, any other letter or digit listed in the section will further identify the section and being liked to another section of the class with the same letter and/or digit combination. Further information on sections is available from academic advisers during registration periods.
The paragraph description briefly indicates the contents and coverage of the course. A detailed course syllabus may be available by request from the office of the offering department.
“Prerequisites” are courses (or their equivalents) that must be completed before registering for the described course. “Co-requisites” are courses taken concurrently with the described course.
The notation “Also listed…” indicates that the course is also given under the number shown. This means that two or more departments or programs sponsor the described course and that students may register under either number, usually the one representing the student’s major program. Classes are jointly delivered. |
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Technology Management and Innovation |
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MG-UY 4204 Management Science 4 Credits
This course teaches students to create mathematical models of managerial problems. Types of models discussed include linear programming, integer-linear programming, non-linear programming, queuing models, decision-tree models, game-theoretic models, simulation models, inventory models and more. Each model is discussed in the context of the assumptions necessary for modeling and the robustness of the model’s managerial recommendations.
Prerequisite(s): 8 credits of calculus: MA-UY 1024 or MA-UY 1054 or MA-UY 1324 and MA-UY 1124 or MA-UY 1154 or MA-UY 1424 or any NYU Tandon Department of Mathematics approved Calculus I (4 cr) and Calculus II (4 cr) courses. Also MA-UY 2054 or MA-UY 2224 or MA-UY 2212 and MA-UY 2222 .
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4214 Financial Strategy 4 Credits
This course deals with the financial strategy of modern firms. Topics include planning and implementation of financial strategies for start-up businesses and the utilization of venture capital; diverse issues related to designing financial strategies of rapidly growing companies after experiencing an IPO; challenges in constructing a financial strategy while undergoing a major corporate restructuring; key components of financial strategies for companies facing rapidly changing technological and competitive environments; and development of financial strategies for mature companies and declining business.
Prerequisite(s): MG-UY 2204 , MG-UY 3204 and MG-UY 3214 .
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4404 Entrepreneurship 4 Credits
This course focuses on key aspects of entrepreneurship as a critical engine for innovation. It also treats entrepreneurship as a state of mind that is not limited to small firms. Students discuss current theories and practices related to starting and managing entrepreneurial enterprises, emphasizing firms in technology-, information- and knowledge-intensive environments. Particular attention is paid to the critical issues of (1) identifying opportunities that provide competitive advantage; (2) the development of a solid business plan; (3) the marketing of new ventures; (4) entrepreneurial business operations, including human-resource and process management; (5) ethical and social issues in entrepreneurial firms; and (6) financial management and fund raising for entrepreneurial firms.
Prerequisite(s): Junior or senior student status.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4504 Global Perspectives on Technology Management: A Capstone Project Course 4 Credits
This course provides students with knowledge of current theories and practices related to managing international and multinational firms. Students study the ways in which international management differs from the management of a firm residing solely within domestic boundaries. Topics covered include planning, organizing, HR management, communication and negotiation and coordination and control of international endeavors. Case studies are used extensively to focus the class on technological examples of problems in international management. Students undertake a term project that either (1) develops a business plan for a technological international venture, (2) creates a case study of a technological firm’s challenges in international management, or (3) analyzes a technological industry’s position vis-à-vis international management.
Prerequisite(s): MG-UY 3002 , MG-UY 3024 , MG-UY 3204 , MG-UY 3404 , and either MG-UY 3214 or MG-UY 3304 .
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4514 Honors Capstone Project in Technology, Innovation and/or Information Management and Entrepreneurship I 4 Credits
In this course, qualified honors students work with a faculty member (and perhaps graduate students) on an advanced topic in technology, innovation and/or information management or entrepreneurship. This effort may be directed toward developing theory, developing case material, or developing a business plan and business strategy for a new venture, or another project of this caliber. A Thesis may compose part of this Honor’s Capstone course.
Prerequisite(s): Senior status, 3.6 GPA or better through the junior year in major; all courses specified by the project adviser.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4524 Honors Capstone Project in Technology, Innovation and/or Information Management Or Entrepreneurship II 4 Credits
In this course, qualified honors students work with a faculty member (and perhaps graduate students) on an advanced topic in technology, innovation and/or information management or entrepreneurship. This effort may be directed toward developing theory, developing case material or developing a business plan and business strategy for a new venture, or another project of this caliber. A Thesis may compose part of this Honor’s Capstone course.
Prerequisite(s): Senior status, 3.6 GPA or better through the junior year in major; all courses specified by the project adviser including MG-UY 4514 .
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4603 Technology Management-Internship and Service 3 Credits
This course provides undergraduate students with the opportunity to learn by working in the field under faculty supervision. This course exposes undergraduates to relevant, state-of-the-art and best practices in modern technology management from the perspective of reflective involvement and interaction in the field. In addition, a service often may be a significant part of this course. The course occurs largely in the field. This course may be taken only once. A member of the TM & I faculty oversees this course; but other faculty members may be involved in directing specific field assignments. This course is open to all BTM majors and requires the permission of the Program Director of the BTM Program.
Note: Students may enroll in a maximum of 3 total internship related credits which will only count as a Free Elective.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MG-UY 4904 BS Thesis in Business and Technology Management 4 Credits
BTM students who earn an overall 3.0 GPA and a 3.4 GPA or better in MG-UY management courses through their junior year of study qualify for an optional thesis. They are advised to meet with the TM&I Department Chair or BTM Program Director in advance of completing their junior year. Before registering for the BTM Thesis, the student must find a Technology Management and Innovation Department full-time faculty member agreeing to serve as thesis adviser and then receive the TM&I Department Head’s approval in writing before proceeding. BTM Thesis students are permitted to replace either the Honor’s Capstone Project I MG-UY 4514 or Honor’s Capstone Project II MG-UY 4524 with MG 4904. This course cannot be repeated.
Prerequisite(s): Overall 3.0 GPA and a 3.4 GPA or better in MG-UY courses through their junior year.
Note: TM Department Chair approval.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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PL-UY 4052 Business Ethics 2 Credits
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Manufacturing Engineering Graduate Courses
The courses with MN designations below are followed by courses from other programs that commonly are taken by manufacturing engineering students. |
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MN-GY 6113 Quality Control and Improvement 3 Credits
This course provides students with a solid foundation in the cost of quality, quality assurance and quality management. Emphasis is placed on the basic tools of quality control such as control charts and their use, the concept of “out of control,” acceptance sampling, variables and attributes charts, and producer’s and consumer’s risk. This course uniquely demonstrates the power of teams of people with different expertise to improve quality. A course project is required.
Prerequisite(s): MA-GY 6513 or equivalent.
Also listed under: IE-GY 6113 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 6123 Quality Engineering Using Robust Design 3 Credits
This course reviews broadly the procedures involved in improving the quality of manufacturing. By employing both Taguchi techniques, such as the use of signal-to-noise ratio representations and other techniques less sensitive to parameter interactions, a full spectrum of robust design methods are presented. Applications of these procedures are reviewed, including online troubleshooting methods to assure quality in manufacturing.
Prerequisite(s): MN-GY 6113 or IE-GY 6113 .
Also listed under: IE-GY 6123 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 6303 Operations Management 3 Credits
This course examines analytical techniques to design and operate production and service systems, including facility layouts and locations, capacity planning, job sequencing, inventory control and quality control. Topics include introductory linear programming and other formal methods. Students use computers and case studies.
Also listed under: MG-GY 6303 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 6323 Building High Performance Teams 3 Credits
Successful manufacturing programs require the teaming of a number of professionals having a variety of types of expertise, such as product design, manufacturing-process design, production engineering, quality control, testing and packaging. In the past, these individual experts were involved only in a serial fashion in the overall product realization process, with not very effective results. Considerable evidence suggests that uniting these experts in a consistent team produces substantial benefits. This course provides students with the skills and knowledge to build work-unit effectiveness. Topics include diagnosing team functioning, understanding group dynamics, and creating a productive team culture, surfacing and resolving critical issues, and implementing strategies for organizational support.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 6513 Design Strategies 3 Credits
Product design is a major determinant of product cost, quality and customer satisfaction. This course explores the design process, including establishing customer requirements and developing product specifications, conceptual design, detailed design, design for manufacturability, competitive analysis and design for the environment. Computer-aided applications and case studies are reviewed.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7503 Introduction to Target Costing—Customer Driven Product Design 3 Credits
Target Costing is a disciplined process for determining and realizing a total cost at which a product with specified functionality must be produced to generate the desired profitability at its anticipated selling price. This course presents both the theoretical foundation and the practical application of Target Costing methodology to the product-realization process. The topics include basic accounting, principles of Target Costing, the Target Costing Process, quantifying the customer requirements, defining the product feature set, price forecasting, experience curves, cost- functionality tradeoffs and implementation check lists. The course includes a hands-on design project in which teams of students will apply the principles of target costing to design a new product.
Note: Online version available.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7713 Product Realization Process 3 Credits
Getting new products developed and to market is a major factor in determining global competitiveness. This course uses case studies to illustrate the product-realization process and the successful application of R&D, concurrent engineering, cross-functional teams, continuous improvement, computer applications, target costing and management of new product development.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7763 Manufacturing Resources Planning 3 Credits
This course discusses computerized systems to run a manufacturing business effectively. Also discussed are the process of software specification, evaluation, selection and implementation. Other topics include manufacturing resources planning logic, enterprise resource planning, manufacturing-execution systems, inventory management and bill of materials. Several software systems and their features are highlighted.
Also listed under: IE-GY 7763 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7853 Computer Integrated Manufacturing Systems (CIMS) 3 Credits
This course introduces the basic concepts of manufacturing products with complex processes that rely heavily on computer and data-processing technologies. All aspects relative to products and processes-planning, design, manufacturing, shipping are addressed from a variety of perspectives. Techniques to manage and optimize manufacturing productivity are explored.
Also listed under: IE-GY 7853 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7873 Lean Manufacturing 3 Credits
This course provides an overview to the basic principles, and theories of lean manufacturing which involves identifying and eliminating non-value-adding activities in design, production, and supply chain management. Students will learn an integrated approach to efficient manufacturing with emphasis on synchronized product, quick changeover, cell design, visual factory, value stream, one-piece flow and understand the metrics used to monitor performance.
Also listed under: IE-GY 7873 .
Note: Online version available.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7883 Manufacturing Systems Engineering 3 Credits
This course concentrates on contemporary techniques for product design and manufacture, including financials of the manufacturing firm, quality, reliability, Taguchi methods of product and process design, scale up and partitioning, production flows, modern manufacturing methods such as Just- In-Time/Total-Quality-Control, pull and synchronized manufacturing. Cultural factors are also discussed.
Also listed under: IE-GY 7883 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7893 Production Science 3 Credits
This course reviews just-in-time and synchronous manufacturing methods. It analyzes the basic dynamics of factories to understand the importance of congestion and bottleneck rates on cycle time and inventories. Analytical models are developed to study variability and randomness introduced by breakdown, setups and batching. Simulation studies are used to provide data on performance of transfer lines.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7923 Design for Manufacturability 3 Credits
This course introduces concepts and techniques for economical, functionally sound and high-quality product design for manufacture. The emphasis is on designing for easy robotic and manual assembly, and on using plastics effectively to reduce manufacturing costs. Managerial and organizational approaches and case studies of successful designs are reviewed.
Also listed under: IE-GY 7923 .
Note: Online version available.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7933 Environmental Health and Safety 3 Credits
This course presents an overview of environmental, health and safety management. Students are introduced to management systems within a manufacturing operation. The course explores the motivations and strategies for environmental, health and safety management. Students learn about the mandatory standards along and about the technical and legal rationale for insuring that workers have a safe and healthy workplace. Because workers safety and health are protected by laws, these skills are needed to work effectively in operations; human resources and employee development as well as industrial relations.
Also listed under: IE-GY 7933 .
Note: Online version available.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7943 Physical Design of Products 3 Credits
This graduate course is offered irregularly in response to industry demand.
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MN-GY 7953 Basics of Supply Chain Operations Management 3 Credits
Supply chain operations seeks to integrate and accelerate the flow of materials, information and cash, throughout the process of supplying goods or services. Supply chain operations optimizes the efforts of suppliers, manufacturers, warehouses, distributors, retailers and customers to create an efficient and robust process. On the service side the same concepts prevail with the suppliers, institutions, providers, administrators and customers. All businesses are part of a supply chain, and understanding and realizing this relationship leads to economies of time, mate- rial, money and improved customer service.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7963 Electronics Systems Manufacturing 3 Credits
In this course, students understand that the physical design and manufacturability of modern electronics systems results from tradeoffs involving partitioning, electrical performance, cooling and mechanical stresses. Design parameters are derived to study the tradeoffs, along with specific examples from reverse-engineering studies. The current status and future directions of low-cost, high-volume manufacturing technologies are examined.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7983 Supply Chain Infrastructure 3 Credits
Effective supply chain operations require well designed, quality products, and the echelons of the supply chain must operate as a team. These elements, also termed the infrastructure, are presumed to exist. The objective of this course is to provide detailed information on the infrastructure elements required to operate a competitive supply chain. This infrastructure will cover product design and development, quality, employee involvement and communication, supplier and customer relationships, logistics, warehousing, information technology and e-business. Among the topics covered in detail will be product realization process and product design; house of quality; quality improvement process; six sigma; kaizan; employee motivation; communication and team dynamics; logistics including networks, third and fourth party organizations; warehousing, including optimum location, innovative information technology and e-business models.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 7993 Supply Chain Engineering 3 Credits
Students in this course gain an understanding of how companies plan, source, make and deliver their products with a global competitive advantage. The course stresses the engineering components in developing an integrated supply chain that covers the entire manufacturing enterprise. It looks at the supply-chain infrastructure and the velocities of different models. The focus is on understanding and detecting the constraints of the infrastructure and the lowest common denominator of the information system used. Students also gain an understanding of logistical networks and the optimizing of the various traffic and location alternatives. Synchronization of supply and demand is examined in detail, looking at variability in both processes with the objective of maximizing throughput and capacity, emphasizing partnering, e-commerce and the bullwhip effect. Finally, the course establishes global performance measurements that compare companies in different industries.
Also listed under: IE-GY 7993 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 8023 Thermal Design of Electronics System for Performance and Reliability
This graduate course is offered irregularly in response to industry demand.
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MN-GY 8043 Thermal Issues in Manufacturing Processes
This graduate course is offered irregularly in response to industry demand.
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MN-GY 8643 New Product Development 3 Credits
This course examines the dynamics of technology and the pressures of competition that drive enterprises to make their product-development and production processes strategically more effective and economically more cost and time efficient. The course covers the state of the art in new product activities for services and manufacturing firms. It also examine in-depth the linkages among marketing, technology and manufacturing technology.
Also listed under: MG-GY 8643 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 8653 Managing Technological Change and Innovation 3 Credits
This course focuses on how to manage effectively technological change and innovation by using a dual perspective. One perspective is based on individual, group and organizational theory, research and practice. This body of literature, viewpoints and experience provides essential guides to manage successfully the introduction of new technologies. Realizing the full potential of new technologies requires managing change effectively to assure 100 percent stakeholder commitment. The second perspective is based on innovation theory, research and practice. This body of literature, viewpoints and experience provides key insights to manage effectively the process of innovation and the impact of innovation on all parts of an enterprise. Specifically, explicit consideration is given to a firm’s to manage and inspire people so that they can communicate and innovate effectively.
Also listed under: MG-GY 8653 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 9113 Selected Topics in Manufacturing Engineering I 3 Credits
Areas not covered in other courses. Specific topics vary according to the instructor, who may be a visiting professor. Topics and prerequisites are announced during the term before the offering.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 9123 Selected Topics in Manufacturing Engineering II 3 Credits
Areas not covered in other courses. Specific topics vary according to the instructor, who may be a visiting professor. Topics and prerequisites are announced during the term before the offering.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MN-GY 9303 Readings in Manufacturing Engineering I 3 Credits
In this course, students read selected papers and current literature in specialized area of study and are guided by a faculty member. The topic must be beyond the scope of regularly offered courses. The topic must be agreed upon by the student and adviser before registration. A written report on the topic is required.
Prerequisite(s): Approval of adviser, instructor and department head.
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MN-GY 9313 Readings in Manufacturing Engineering II 3 Credits
In this course, students read selected papers and current literature in specialized area of study and are guided by a faculty member. The topic must be beyond the scope of regularly offered courses. The topic must be agreed upon by the student and adviser before registration. A written report on the topic is required.
Prerequisite(s): Approval of adviser, instructor and department head.
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MN-GY 9963 MS Report I 3 Credits
This course is an independent project that demonstrates a student’s professional maturity and graduate-level knowledge. Students, guided by an adviser, are expected to demonstrate experimental work, software development and extensive analyses. A student’s report must include results in one or more of these areas: critical analysis and interpretation of pertinent literature. A required written report (unbound) should represent a worthy contribution.
Prerequisite(s): Adviser’s approval.
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MN-GY 9973 MS Report II 3 Credits
With approval by the graduate adviser, some students may take a 6-credit MS report. This report should be planned during registration for MN-GY 9963 . In such cases, MN 9973 is used for the second half of the registration. A grade of S or U is awarded in MN-GY 9963 in these cases, and the letter grade given in MN 9973 applies to all 6 credits.
Prerequisite(s): Adviser’s approval.
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Materials Science |
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ME-UY 2811 Materials Science Laboratory 1 Credits
Students learn to characterize the microstructure and crystal structure of a material by optical and scanning electron microscopy and X-ray diffraction. The mechanical characterization is accomplished by hardness, tensile and yield strength, impact and fatigue testing.
Prerequisite(s): PH-UY 1013 and CM-UY 1004 (or CM-UY 1014 and CM-UY 1024 ). Corequisite(s): ME-UY 2813 .
Weekly Lecture Hours: 0.5 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 1.5
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ME-UY 2813 Introduction to Materials Science 3 Credits
Students in this course become familiar with atomic structure and bonding, atomic arrangement in crystals, crystal imperfections, mechanical behavior and failure of materials and binary phase diagrams.
Prerequisite(s): PH-UY 1013 and CM-UY 1004 (or CM-UY 1014 and CM-UY 1024 ). Corequisite(s): ME-UY 2811 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MT-UY 4853 Manufacturing Engineering and Processes 3 Credits
This course introduces the manufacturing processes for fabricating components used in mechanical systems; casting processes; bulk metal deformation and sheet-metal forming processes; materials-removal processes; Joining and fastening processes; manufacturing automation; and integrated manufacturing systems.
Prerequisite(s): ME-UY 2811 and ME-UY 2813 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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Mathematics |
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MA-GY 942X Reading in Mathematics II 1-3 Credits
In this course, reading is guided by faculty members and devoted mainly to scholarly papers. | Offered every term.
Prerequisite(s): Department’s permission.
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MA-GY 997X MS Thesis in Math 3-9 Credits
In this course, students present a thesis of independent investigation of a suitable problem in mathematics. Study must include adequate investigation of existing literature relating to the subject. Regular reports on progress of work and regular conferences with assigned faculty adviser are required. | Offered every term.
Prerequisite(s): Degree status.
Note: Re-registration fee, any part: 3-credit charge.
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MA-GY 999X PhD Diss. in Math 3-12 Credits
Offered every term.
Prerequisite(s): Passing the Qualifying Examination.
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MA-GY 6213 Elements of Real Analysis I 3 Credits
This course and its sequel MA-GY 6223 rigorously treat the basic concepts and results in real analysis. Course topics include limits of sequences, topological concepts of sets for real numbers, properties of continuous functions and differentiable functions. Important concepts and theorems include supremum and infimum, Bolzano-Weierstrass theorem, Cauchy sequences, open sets, closed sets, compact sets, topological characterization of continuity, intermediate value theorem, uniform continuity, mean value theorems and inverse function theorem. | Offered in the fall.
Prerequisite(s): MA-UY 2122 or permission of adviser.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 6223 Elements of Real Analysis II 3 Credits
This course continues MA-GY 6213 . The topics are integration, series of real numbers, sequences and series of functions and Fourier series. Important concepts and theorems include Riemann and Riemann-Stieltjes integral, fundamental theorem of calculus, the mean value theorem of integrals, Dirichlet test, absolute and conditional convergence, uniform convergence, Weierstrass test, power series, orthogonal functions and Fourier series. | Offered in the spring.
Prerequisite(s): MA-GY 6213 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 7033 Linear Algebra I 3 Credits
This course covers basic ideas of linear algebra: Groups, rings, fields, vector spaces, basis, dependence, independence, dimension. Relation to solving systems of linear equations and matrices. Homomorphisms, duality, inner products, adjoints and similarity. | Offered in the fall.
Prerequisite(s): MA-UY 2034 and MA-UY 2114 or Graduate Standing.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 7043 Linear Algebra II 3 Credits
This course continues MA-GY 7033 . Topics covered are basic concepts of linear algebra continuing with: range, nullity, determinants and eigenvalues of matrices and linear homomorphisms, the polar decomposition and spectral properties of linear maps, orthogonality, adjointness and its applications. | Offered in the spring.
Prerequisite(s): MA-GY 7033 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 9413 Reading in Mathematics I 3 Credits
In this course, reading is guided by faculty members and devoted mainly to scholarly papers. | Offered every term.
Prerequisite(s): Department’s permission.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 9433 Reading in Mathematics III 3 Credits
In this course, reading is guided by faculty members and devoted mainly to scholarly papers. | Offered every term.
Prerequisite(s): Department’s permission.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 9443 Reading in Mathematics IV 3 Credits
In this course, reading is guided by faculty members and devoted mainly to scholarly papers. | Offered every term.
Prerequisite(s): Department’s permission.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-GY 9453 Reading in Mathematics V 3 Credits
In this course, reading is guided by faculty members and devoted mainly to scholarly papers. | Offered every term.
Prerequisite(s): Department’s permission.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 492X Independent Study 1-4 Credits
In this course, students read, study and investigate selected topics in mathematics. Students discuss and present problems. | Offered in fall and spring.
Prerequisite(s): Departmental adviser’s approval.
Note: This course is repeatable for credit.
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MA-UY 914 Precalculus for Engineers 4 Credits
This course covers: foundations of algebra, exponents, multiplication of algebraic expressions, factoring algebraic expressions, working with algebraic fractions, proportionality, rates of change, equations of lines, completing squares, the quadratic formula, solving equations, systems of linear equations, inequalities, domain and range of functions, exponential and logarithmic functions, compositions of functions, transformations of functions, right triangles, trigonometry of triangles. | Offered every term.
Prerequisite(s): Diagnostic exam Corequisite(s):
Note: Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 954 Precalculus 4 Credits
This course covers the fundamentals of algebra with a focus on Management and the Life Sciences. The topics include: foundations of algebra, solving equations, exponents, working with algebraic expressions, working with algebraic fractions, proportionality, rates of change, lines in the plane, completing squares, the quadratic formula, systems of linear equations, inequalities, graphs, exponentials, logarithms, inverses of functions, compositions of functions, transformations of functions, and right angle trigonometry. | Offered every term.
Prerequisite(s): Diagnostic exam Corequisite(s):
Note: Course required only for specific Majors in place of MA-UY 914. Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1002 The Art of Mathematics 2 Credits
This is an introductory course about Mathematics. Areas of Mathematics. History of Mathematics. Mathematical Methods. Great Mathematicians. Famous open and solved mathematical problems. The study of Mathematics. Mathematical Software. | Offered in the fall.
Prerequisite(s): Only first-year students are permitted to enroll in this introductory level course.
Weekly Lecture Hours: 2 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1022 Calculus IB 2 Credits
In this course the foundations of calculus are studied by investigating functions and their rates of change. Building on a previous knowledge of limits and derivatives, the derivative is studied in more depth with an emphasis on applications and modeling in science and engineering. Applications include rates and related rates, optimization, modeling, and indeterminate forms. The definite integral is introduced as a measure of the total accumulation of a function over an interval, and the course concludes with a study of the Fundamental Theorem of Calculus which links differentiation and integration. | Offered every term.
Prerequisite(s): AP credit or MA-UY 1012 or MA-UY 1054. Corequisite(s): EX-UY 1 Examination Hour
Weekly Lecture Hours: 2
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MA-UY 1024 Calculus I for Engineers 4 Credits
This course covers: Library of functions, functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rules, the chain rule, applications of the chain rule, maxima and minima, optimization.The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics. | Offered every term.
Prerequisite(s): Diagnostic exam or MA-UY 912 or MA-UY 914 . Corequisite(s):
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1054 Calculus I with Precalculus 4 Credits
This course covers limits, definition of the derivative, differentiation rules for polynomial and trigonometric functions, applications of the chain rule and introduction to optimization with a focus on Management and the Life Sciences. | Offered every term.
Prerequisite(s): Diagnostic exam or MA-UY 912 or MA-UY 954 or equivalent. Corequisite(s):
Note: Course required only for specific Majors in place of MA-UY 1024/1324.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1124 Calculus II for Engineers 4 Credits
This course covers techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics. | Offered every term.
Prerequisite(s): MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better). Corequisite(s):
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1132 Numerical Methods for Calculus 2 Credits
Functions of Two Variables, and their Graphs. Contour Diagrams. Linear Functions and Functions of Three Variables. Limits and Continuity of functions of two and three variables. Areas and Volumes. Basic Integration methods and Numerical Methods for Definite Integrals. Improper Integrals. Convergence of Series. Power Series. Taylor Polynomial and series. Applications. | Offered in the fall and the spring.
Prerequisite(s): AP credit or transfer credit for Calculus I and II or MA-UY 1112 or (MA-UY 1054 and MA-UY 1154 ). Corequisite(s):
Weekly Lecture Hours: 2 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1154 Calculus II with Precalculus 4 Credits
This course covers the first and second derivatives, optimization problems, antiderivatives, Fundamental Theorem of Calculus, techniques of integration, logarithmic and exponential functions, numerical methods of integration, applications of integration, introduction to differential equations, and introduction to series with a focus on Management and the Life Sciences. | Offered every term.
Prerequisite(s): MA-UY 1054 . Corequisite(s):
Note: Course required only for specific Majors in place of MA-UY 1124/1424.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1324 Integrated Calculus I for Engineers 4 Credits
This course covers: Library of Functions, functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics. | Offered every term.
Prerequisite(s): Disgnostic exam or MA-UY 912 or MA-UY 914 . Corequisite(s):
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 1424 Integrated Calculus II for Engineers 4 Credits
This course covers techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics. | Offered every term.
Prerequisite(s): MA-UY 1022 or MA-UY 1024 or MA-UY 1324 . Corequisite(s):
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 2034 Linear Algebra and Differential Equations 4 Credits
MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, Matrix Theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science. | Offered every term.
Prerequisite(s): MA-UY 1124 or MA-UY 1132 or MA-UY 1424 .
Note: Not open to students who have taken MA-UY 3044 or MA-UY 3054 or MA-UY 3083 or MA-UY 4204.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0
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MA-UY 2054 Applied Business Data Analysis I 4 Credits
This course covers applications of theories of random phenomena to problems in business management. Topics include probability theory, discrete and continuous probability distributions, sampling, measures of central value and dispersion, sampling distributions, statistical estimation and introduction to hypothesis testing. Use of statistical software is integrated with the previous topics; examples are drawn from problems in business decision-making. Applications to advanced statistical applications in business management. Emphasis is on application of concepts. Use of statistical software integrated with the previous topics. | Offered in the spring.
Prerequisite(s): MA-UY 1054 or equivalent.
Note: Course required only for Management Majors. Credit for this course may not be used to satisfy the requirements for other majors.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 2114 Calculus III: Multi-Dimensional Calculus 4 Credits
Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes. | Offered every term.
Prerequisite(s): MA-UY 1124 or MA-UY 1132 or MA-UY 1424
Weekly Lecture Hours: 4
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MA-UY 2224 Data Analysis 4 Credits
An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distribution of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course. | Offered every term.
Prerequisite(s): MA-UY 1124 or MA-UY 1132 or MA-UY 1424
Note: Not open to students who have taken MA-UY 2233 or MA-UY 3012 or MA-UY 3022.
Weekly Lecture Hours: 4
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MA-UY 2233 Introduction to Probability 3 Credits
Standard first course in probability, recommended for those planning further work in probability or statistics. Probability of events, random variables and expectations, discrete and continuous distributions, joint and conditional distributions, moment generating functions, the central limit theorem. | Offered every term.
Prerequisite(s): MA-UY 109 or MA-UY 2112 or MA-UY 2114 .
Also listed under: ECE-UY 2233
Note: Not open to students who have taken MA-UY 2224 or MA-UY 3012 or MA-UY 3022.
Weekly Lecture Hours: 3
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MA-UY 2314 Discrete Mathematics 4 Credits
Logic, proofs, set theory, functions, relations, asymptotic notation, recurrences, modeling computation, graph theory. | Offered in the fall and the spring.
Prerequisite(s): Math Diagnostic Exam or MA-UY 912 or MA-UY 914 (minimum calculus level required) OR MATH-SHU 110 (for Shanghai Students)
Note: This course and CS-GY 6003 cannot both be taken for credit.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 2414 Basic Practice of Statistics 4 Credits
We are inundated by data, but data alone do not translate into useful information. Statistics provides the means for organizing, summarizing, and therefore better analyzing data so that we can understand what the data tell us about critical questions. If one collects data then understanding how to use statistical methods is critical, but it is also necessary to understand and interpret all the information we consume on a daily basis. This course provides these basic statistical approaches and techniques. This course may not be acceptable as a substitute for any other Probability and Statistics course. For Sustainable Urban Environments (SUE) students, please see your advisor. | Offered in the fall and the spring.
Prerequisite(s): None
Note: This course does not count towards degree if student has already taken MA-UY 2224 or MA-UY 2054.
Weekly Lecture Hours: 4
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MA-UY 3014 Applied Probability 4 Credits
An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, the Central Limit Theorem and Laws of Large Numbers, Markov Chains, and basic stochastic processes | Offered in the fall and spring.
Prerequisite(s): A grade of C or better in MA-UY 2114 and (MA-UY 2034 or MA-UY 3034 or MA-UY 3044 or MA-UY 3054 ).
Also listed under: MATH-UA 233 Theory of Probability
Note: Not open to students who have taken MA-UY 2224, MA-UY 2233/EE-UY 2233, or MA-UY 3022.
Weekly Lecture Hours: 4
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MA-UY 3022 Probability Theory II 2 Credits
This course covers multivariate random variables, moment generating functions, properties of expectation, limit theorems and gives an introduction to random processes and their applications. | Offered in the fall and the spring.
Prerequisite(s): MA-UY 2224 or MA-UY 3012
Note: Not open to students who have taken MA-UY 2233.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 3034 Applied Linear Algebra 4 Credits
Systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and least squares fit, singular value decompositions, computational techniques, conditioning, pseudo-inverses.
Prerequisite(s): MA-UY 1024 or MA-UY 1324
Weekly Lecture Hours: 4
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MA-UY 3044 Linear Algebra 3-4 Credits
Systems of linear equations, Gaussian elimination, matrices, determinants, Cramer’s rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms. Restricted to Tandon math and CS majors and students with a permission code from the math department. Fulfills linear algebra requirement for the BS Math and BS CS degrees. | Offered every term.
Prerequisite(s): A grade of C or better in MA-UY 1022 or MA-UY 1024 or MA-UY 1324 .
Also listed under: MATH-UA 140 Linear Algebra.
Note: Not open to students who have taken MA-UY 1533, MA-UY 2034, MA-UY 3054, or MA-UY 3113.
Weekly Lecture Hours: 4
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MA-UY 3054 Honors Linear Algebra 4 Credits
This honors section of Linear Algebra is intended for well-prepared students who have already developed some mathematical maturity. Its scope will include the usual Linear Algebra (MA-UY 3044 ) syllabus; however, this class will move faster, covering additional topics and going deeper. Vector spaces, linear dependence, basis and dimension, matrices, determinants, solving linear equations, eigenvalues and eigenvectors, quadratic forms, applications such as optimization or linear regression. | Offered in the fall and the spring.
Prerequisite(s): A grade of A- or better in MA-UY 1022 or MA-UY 1024 or MA-UY 1324 .
Also listed under: MATH-UA 148 Honors Linear Algebra.
Note: Not open to students who have taken MA-UY 1533, MA-UY 2034, MA-UY 3044, or MA-UY 3113.
Weekly Lecture Hours: 4
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MA-UY 3113 Advanced Linear Algebra and Complex Variables 3 Credits
This course provides a deeper understanding of topics introduced in MA-UY 2012 and MA-UY 2034 and continues the development of those topics, while also covering functions of a Complex Variable. Topics covered include: The Gram-Schmidt Process, inner product spaces and applications, singular value decomposition, LU decomposition. Derivatives and Cauchy-Riemann equations, integrals and Cauchy integral theorem. Power and Laurent Series, residue theory. | Offered in the fall and the spring.
Prerequisite(s): (MA-UY 2114 or MA-UY 2122 ) and (MA-UY 2012 or MA-UY 2034 ).
Note: Not open to students who have taken MA-UY 1533, MA-UY 3112, or MA-UY 4433.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 3914 Project in Mathematics I 4 Credits
This course is repeatable for credit, but does not allow multiple enrollment in the same term. | Offered in the fall and the spring.
Prerequisite(s): Approval of departmental adviser.
Note: This course is repeatable for credit, but does not allow multiple enrollment in the same term.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 4014 Theory of Numbers 4 Credits
Divisibility and prime numbers. Linear and quadratic congruences. The classical number-theoretic functions. Continued fractions. Diophantine equations. | Offered in the fall.
Prerequisite(s): A grade of C or better in MA-UY 1124 or MA-UY 1132 or MA-UY 1424 .
Also listed under: MATH-UA 248 Theory of Numbers
Weekly Lecture Hours: 4
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MA-UY 4044 Algebra 4 Credits
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, homomorphisms and quotient groups. Rings and quotient rings, Euclidean rings, polynomial rings. Fields, finite extensions. | Offered in the fall and the spring.
Prerequisite(s): A grade of C or better in MA-UY 4613 and (MA-UY 3044 or MA-UY 3054 or MA-UY 3113 ), or permission of instructor.
Also listed under: MATH-UA 343 Algebra
Note: Cannot receive credit for both MA-UY 4044 and MA-UY 4054.
Weekly Lecture Hours: 4
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MA-UY 4054 Honors Algebra I 4 Credits
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, group actions, homomorphisms and quotient groups, direct products, classification of finitely generated abelian groups, Sylow theorems. Rings, ideals and quotient rings, Euclidean rings, polynomial rings, unique factorization. | Offered in the fall.
Prerequisite(s): A grade of B or better in MA-UY 4613 and (MA-UY 3044 or MA-UY 3054 or MA-UY 3113 ) or instructor permission.
Also listed under: MATH-UA 348 Honors Algebra I
Note: Cannot receive credit for both MA-UY 4044 and MA-UY 4054.
Weekly Lecture Hours: 4
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MA-UY 4064 Honors Algebra II 4 Credits
Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals. | Offered in the spring.
Prerequisite(s): A grade of C or better in MA-UY 4054 or (a grade of A in MA-UY 4044 and instructor permission).
Also listed under: MATH-UA 349 Honors Algebra II
Weekly Lecture Hours: 4
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MA-UY 4114 Applied Statistics 4 Credits
An introduction to the mathematical foundations and techniques of modern statistical analysis for the interpretation of data in the quantitative sciences. Mathematical theory of sampling; normal populations and distributions; chi-square, t, and F distributions; hypothesis testing; estimation; confidence intervals; sequential analysis; correlation, regression; analysis of variance. Applications to the sciences. Use of Matlab for doing computations of the statistical measures listed above.
Prerequisite(s): MA-UY 3014 or MA-UY 2233
Weekly Lecture Hours: 4
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MA-UY 4204 Ordinary Differential Equations 3-4 Credits
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: first-order equations including integrating factors; second-order equations including variation of parameters; series solutions; elementary numerical methods including Euler’s methods, Runge-Kutta methods, and error analysis; Laplace transforms; systems of linear equations; boundary-value problems. Restricted to Tandon math majors and students with a permission code from the math department. Fulfills ordinary differential equations requirement for the BS Math degree. | Offered in the fall and the spring.
Prerequisite(s): A grade of C or better in MA-UY 2114 and (MA-UY 3044 or MA-UY 3054 or MA-UY 3113 ).
Also listed under: MATH-UA 262 Ordinary Differential Equations
Note: Not open to students who have taken MA-UY 2034 or MA-UY 3083.
Weekly Lecture Hours: 4
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MA-UY 4214 Applied Ordinary Differential Equations 4 Credits
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: first-order equations including integrating factors; second-order equations including variation of parameters; series solutions; elementary numerical methods including Euler’s methods, Runge-Kutta methods, and error analysis; Laplace transforms; systems of linear equations; boundary-value problems. Restricted to Tandon math majors and students with a permission code from the math department. Fulfills ordinary differential equations requirement for the BS Math degree.
Prerequisite(s): MA-UY 2114 and (MA-UY 3034 or MA-UY 3044 or MA-UY 3054 ).
Note: Not open to students who have taken MA-UY 2034 or MA-UY 4204.
Weekly Lecture Hours: 4
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MA-UY 4314 Combinatorics 4 Credits
Techniques for counting and enumeration including generating functions, the principle of inclusion and exclusion, and Polya counting. Graph theory. Modern algorithms and data structures for graph-theoretic problems. | Offered in the spring.
Prerequisite(s): A grade of C or better in MA-UY 1124 or MA-UY 1132 or MA-UY 1424 .
Also listed under: MATH-UA 240 Combinatorics
Weekly Lecture Hours: 4
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MA-UY 4413 Applied Partial Differential Equations 3 Credits
Modeling of physical processes. Classification of equations. Formulation and treatment of boundary- and initial-value problems. Green’s functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear first-order equations and characteristics. D’Alembert solution of wave equation. Conservation laws and shock waves. | Offered in the fall and the spring.
Prerequisite(s): MA-UY 2114 and (MA-UY 3083 or MA-UY 4204 ).
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 4414 Applied Partial Differential Equations 3-4 Credits
This course gives an overview of PDEs that occur commonly in the physical sciences with applications in heat flow, wave propagation, and fluid flow. Analytical as well as some numerical solution techniques will be covered, with a focus on applications rather than analysis.
Prerequisite(s): MA-UY 2034 or MA-UY 4204 or MA-UY 4214
Weekly Lecture Hours: 4
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MA-UY 4424 Numerical Analysis 3-4 Credits
In numerical analysis one explores how mathematical problems can be analyzed and solved with a computer. As such, numerical analysis has very broad applications in mathematics, physics, engineering, finance, and the life sciences. This course gives an introduction to this subject for mathematics majors. Theory and practical examples using Matlab will be combined to study a range of topics ranging from simple root-finding procedures to differential equations and the finite element method | Offered in the fall and spring.
Prerequisite(s): A grade of C or better in MA-UY 2114 and (MA-UY 3034 or MA-UY 3044 or MA-UY 3054 or MA-UY 3113 ).
Also listed under: MATH-UA 252 Numerical Analysis
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 4434 Applied Complex Variables 4 Credits
A first course in complex analysis, with a focus on applications. Topics to be covered include the complex plane, analytic functions, complex differentiation, the Cauchy-Riemann equations, branch cuts, contour integration, the residue theorem, conformal mapping, applications to potential theory and fluid flow.
Prerequisite(s): MA-UY 2114 and (MA-UY 2034 or MA-UY 3034 or MA-UY 3044 or MA-UY 3054 ).
Note: Not open to students who have taken MA-UY 3113.
Weekly Lecture Hours: 4
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MA-UY 4444 Intro to Math Modeling 3-4 Credits
Formulation and analysis of mathematical models. Mathematical tools include dimensional analysis, optimization, simulation, probability, and elementary differential equations. Applications to biology, sports, economics, and other areas of science. The necessary mathematical and scientific background will be developed as needed. Students participate in formulating models as well as in analyzing them. | Offered in the fall and the spring.
Prerequisite(s): A grade of C or better in MA-UY 2114 .
Also listed under: MATH-UA 251 Intro to Math Modeling
Note: Not open to students who have taken MA-UY 2393.
Weekly Lecture Hours: 4
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MA-UY 4474 Chaos and Dynamical Systems 4 Credits
Topics will include dynamics of maps and of first order and second-order differential equations, stability, bifurcations, limit cycles, dissection of systems with fast and slow time scales. Geometric viewpoint, including phase planes, will be stressed. Chaotic behavior will be introduced in the context of one-variable maps (the logistic), fractal sets, etc. Applications will be drawn from physics and biology. There will be homework and projects, and a few computer lab sessions (programming experience is not a prerequisite). | Offered in the spring.
Prerequisite(s): A grade of C or better in (MA-UY 1124 or MA-UY 1132 or MA-UY 1424 ) and (MA-UY 3044 or MA-UY 3054 or MA-UY 3113 )
Also listed under: MATH-UA 264 Chaos and Dynamical Systems
Weekly Lecture Hours: 4
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MA-UY 4613 Analysis I 3 Credits
This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, continuity, partial differentiation, extreme value problems with constraints. | Offered in the fall.
Prerequisite(s): (MA-UY 2114 or MA-UY 2122 ) and (MA-UY 2034 or MA-UY 2132 ).
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 4614 Applied Analysis 3-4 Credits
Limits of real and complex sequences and series; topology of metric spaces; continuity and differentiability of functions; definition, properties, and approximations of Riemann integrals; convergence of sequences and series of functions; Fourier series and other orthogonal systems of functions, approximations theorems.
Prerequisite(s): MA-UY 2114 and (MA-UY 2034 or MA-UY 3034 or MA-UY 3044 or MA-UY 3054 ).
Weekly Lecture Hours: 4
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MA-UY 4623 Analysis II 3 Credits
This course covers the study of basic topics in analysis with emphasis on methods. The Riemann integral, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals, sequences, series, uniform convergence, Beta and Gamma functions. | Offered in the spring.
Prerequisite(s): MA-UY 4613 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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MA-UY 4634 Vector Analysis 4 Credits
Brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Lagrange multipliers. Inverse and implicit function theorems and their applications. Introduction to calculus on manifolds: definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss’ and Stokes’ theorems on manifolds. | Offered in the spring.
Prerequisite(s): A grade of C or better in MA-UY 4613 .
Also listed under: MATH-UA 224 Vector Analysis
Weekly Lecture Hours: 4
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MA-UY 4674 Differential Geometry 4 Credits
The geometry of curves and surfaces in Euclidean space. Frenet formulas, the isoperimetric inequality, local theory of surfaces in Euclidean space, first and second fundamental forms. Gaussian and mean curvature, isometries, geodesics, parallelism, the Gauss-Bonnet Theorem. | Offered in the spring.
Prerequisite(s): A grade of C or better in MA-UY 2114 and (MA-UY 3044 or MA-UY 3054 or MA-UY 3113 ).
Also listed under: MATH-UA 377 Differential Geometry
Note: Not open to students who have taken MA-UY 3303.
Weekly Lecture Hours: 4
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MA-UY 4993 B.S. Thesis in Mathematics 3 Credits
The course provides the framework for a bachelor’s thesis. In the Bachelor’s thesis, a student reports on an independent investigation of a topic in Mathematics that demonstrates an in-depth knowledge of that area of Mathematics and proficiency in using its specific methods. | Offered periodically.
Prerequisite(s): Departmental adviser’s approval.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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Mechanical Engineering |
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ME-GY 996X MS Project in Mechanical Engineering variable Credits
This course is an engineering project under faculty guidance. A written project proposal and final report must be submitted to the department head and the adviser and may be extended to a thesis with the project adviser’s recommendation. Credit only upon completion of project.
Prerequisite(s): Degree status.
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ME-GY 997X MS Thesis in Mechanical Engineering variable credit Credits
The master’s thesis presents results of original investigation in the student’s specialty. This effort can be an extension of ME-GY 996X , with approval of the project adviser. Continuous registration is required. Maximum of 9 credits of ME-GY 996X /ME 997x are counted toward the degree.
Prerequisite(s): Degree status.
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