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MATH-UA 9211 Mathematics for Economics I
NYU London
Instructor Information ● Simon Hubbert
Course Information ● Monday, 9am-12pm. ○ Room G05 ● Exposure to high school calculus.
Course Overview and Goals The course will provide the student with a clear exposition of the essential mathematical tools and techniques that are frequently used to solve problems arising in economics.
The course will be delivered by traditional “chalk and talk” lectures and supplemented with regular take home assignments
Upon Completion of this Course, students will be able to: ● master the theory and properties of real valued functions. ● describe an economic problem using mathematical language and then solve using the appropriate mathematical method ● use methods from calculus to find the optimal location and value (maximum/minimum) of a mathematical function.
Course Requirements
Grading of Assignments The grade for this course will be determined according to these assessment components: % of Assignments/ Description of Assignment Final Due Activities Grade Weekly problem sheet based on the most Assignments 20% recent lecture topics
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% of Assignments/ Description of Assignment Final Due Activities Grade 2 hours test: 12 multiple choice questions Mid-term test and 5 free response questions covering 40% the material covered so far 2 hours exam: 12 multiple choice Final questions and 5 free response questions 40% covering the entire sylabus
Failure to submit or fulfill any required course component results in failure of the class
Grades Letter grades for the entire course will be assigned as follows: Letter Percent Description Grade Thorough understanding of both theory and its A 94% and higher applications. A good understanding of the theory and B 84% - 86% confidence in its applications. A good understanding of the theory and C 74% - 76% reasonable competence in its applications. A reasonable understanding of both theory D 65% - 66% and applications. An inability to master both the theory and its F 64% and lower applications to an acceptable level.
Course Materials
Required Textbooks & Materials ● There is no single text for the course the lecture notes are designed to be self- contained
Optional Textbooks & Materials ● Essential Mathematics for Economic Analysis (4th Edition) by Knut Sydsaeter and Peter Hammond with Arne Strom. ISBN 9780273787624 [Nice mixture of theory and examples] ● Mathematics for Economics and Business (7th Edition) by Ian Jacques. ISBN 978- 0273763567. [Many worked examples] ● Mathematics for Economists by Carl P. Simon and Lawrence Blume ISBN 978- 0393117523 [To explore the subject in greater depth]
Resources
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● Access your course materials: NYU Classes (nyu.edu/its/classes) ● Databases, journal articles, and more: Bobst Library (library.nyu.edu) ● NYUL Library Collection: Senate House Library (catalogue.libraries.london.ac.uk) ● Assistance with strengthening your writing: NYU Writing Center (nyu.mywconline.com) ● Obtain 24/7 technology assistance: IT Help Desk (nyu.edu/it/servicedesk)
Course Schedule Assignment Session/Date Topic Reading Due Introductory Lecture upload: Number line, functions Session 1: material. No assignment and Linear Equations
Lecture upload: Properties of functions, supply and demand, theory of quadratic Due Next Session 2: Equation solving. equations, the domain and range of a Lecture mathematical function, economic examples. Lecture upload: Properties of functions, supply and demand, theory of quadratic Mathematical Due Next Session 3: equations, the domain and range of a Functions Lecture mathematical function, economic examples Lecture upload: Equilibrium under tax Equilibrium constraints, continuity of functions, theory and Due Next Session 4: limiting values of functions, practical introduction to Lecture examples of computing limits. limits
Lecture upload: Intermediate value theorem, definition of a derivative, geometric interpretation of derivative (as tangent line to a curve), computing Due Next Session 5: Differentiation derivatives from first principles, locating Lecture a stationary point of a function, economic applications.
Practical problem Session 6: In class problems upload. N/A solving Lecture upload: Rules of differentiability, implicit differentiation, L’hopitals rule for Differentiation computing limits, linear approximations, Due Next Session 7: continued the concept of elasticity with economic Lecture examples.
Lecture upload: Further examples of calculating derivatives, using derivatives Due Next Session 8: Optimization to distinguish the type of stationary Lecture point, max, min or inflection, practical examples. SAMPLE SYLLABUS – SUBJECT TO CHANGE Page 3 SAMPLE SYLLABUS – SUBJECT TO CHANGE
Assignment Session/Date Topic Reading Due
Revision Lecture/ Session 9: Exam practice Review all notes No assignment
Session 10: Mid term test N/A Lecture upload: Further examples of optimization. Properties of functions of several variables, visualization in two- Functions of dimensional context using contour Due Next Session 11: several variables diagrams, notion of the partial Lecture derivatives, the small increments formula and applications
Lecture upload: Mixed derivatives, Functions of stationary points of a function of several several variables variables, classification of stationary Due Next Session 12: continued: points (max, min or saddle point), Lecture economic examples.
Lecture upload: A recipe for finding the Multivariable extreme points of a function of two Due Next Session 13: optimization variables, solution of constrained Lecture problems using the substitution method Lecture upload: A retrospective of the entire course: Revision of key themes Session 14: Retrospective No assignment and exam practice.
Final Final Exam Assessment:
Co-Curricular Activities
• N/A.
Classroom Etiquette • Mobile phones switched off. No hot food.
NYUL Academic Policies
Attendance and Tardiness • Key information on NYU London’s absence policy, how to report absences, and what kinds of absences can be excused can be found on our website (http://www.nyu.edu/london/academics/attendance-policy.html)
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Assignments, Plagiarism, and Late Work • You can find details on these topics and more on this section of our NYUL website (https://www.nyu.edu/london/academics/academic-policies.html) and on the Policies and Procedures section of the NYU website for students studying away at global sites (https://www.nyu.edu/academics/studying-abroad/upperclassmen- semester-academic-year-study-away/academic-resources/policies-and- procedures.html).
Classroom Conduct Academic communities exist to facilitate the process of acquiring and exchanging knowledge and understanding, to enhance the personal and intellectual development of its members, and to advance the interests of society. Essential to this mission is that all members of the University Community are safe and free to engage in a civil process of teaching and learning through their experiences both inside and outside the classroom. Accordingly, no student should engage in any form of behaviour that interferes with the academic or educational process, compromises the personal safety or well-being of another, or disrupts the administration of University programs or services. Please refer to the NYU Disruptive Student Behavior Policy for examples of disruptive behavior and guidelines for response and enforcement.
Disability Disclosure Statement Academic accommodations are available for students with disabilities. Please contact the Moses Center for Students with Disabilities (212-998-4980 or [email protected]) for further information. Students who are requesting academic accommodations are advised to reach out to the Moses Center as early as possible in the semester for assistance.
Instructor Bio Dr Hubbert is a reader in mathematics and mathematical finance at Birkbeck, University of London. He is the author of Essential Mathematics for Market Risk Management (Wiley Finance) and also a former practitioner in financial risk management at the Debt Management Office (a branch of HM-treasury).
His major research interests lie in approximation theory and applications where he has published on a variety of themes.
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