Math Preparation

[eldreddyl]

Below is a list of resources I found useful for developing the mathematical intuition required for economic research

Additionally, I've taken the following courses at Syracuse University. Descriptions are taken from course syllabi

Calculus

• MAT 295: Calculus I
  • Analytic geometry, limits, derivatives, maxima-minima, related rates, graphs, differentials, exponential and logarithmic functions, mean-value theorem, L’Hospital’s rule, integration.
  • Textbook: Essential Calculus: Early Transcendentals, Stewart
• MAT 296: Calculus II
  • Integration: the definite integral and applications; trigonometric functions, method of integration, improper integrals, infinite series, elementary differential equations, parametric equations, polar coordinates
  • Textbook: Essential Calculus: Early Transcendentals, Stewart
• MAT 397: Calculus III
  • Analytic geometry and vectors; functions of more than one variable, multiple integrals, partial differentiation, physical applications, line and surface integrals of scalar functions and vector fields, Green’s, Stokes’, and divergence theorems
  • Textbook: Multivariable Calculus , Stewart

Linear Algebra

• MAT 331: Linear Algebra I
  • Linear equations, n-dimensional euclidean space, linear independence, bases, linear transformations, matrices and determinants, eigenvalues and eigenvectors.
• MAT 531: Linear Algebra II (Proof based)
  • Proofs for results from MAT 331, vector spaces over an arbitrary field, linear transformations, inner products

Analysis

• MAT 375: Introduction to Abstract Mathematics
  • Principles of symbolic logic, set theory, basic function theory, relations, and cardinality. Emphasis on developing proof-writing skills, including mathematical induction.
• MAT 412: Real Analysis I
  • Introduction to the foundations of calculus covering topics from the following: the real number system is a complete ordered field, sequences, limits, Bolzano-Weierstrass, Cauchy sequences, limits of functions, continuity, Extreme Value theorem, Intermediate Value theorem, nowhere continuous functions, uniform continuity. Differentiability of functions of one real variable, Mean value theorem, generalized mean value theorem, L’Hopital’s rule, Taylor’s theorem, Inverse function theorem.

Statistics & Econometrics

• ECN 521: Economic Statistics
• ECN 522: Econometric Methods
• ECN 620: Foundations of Econometrics (Graduate level)
• ECN 621: Econometrics I (Graduate level)
• ECN 623: Econometrics III, Program Evaluation (Graduate Level)

Mathematical Economics

• ECN 505: Mathematical Economics
• ECN 605: Mathematics for Economists (Graduate level)

[eldreddyl]

• The American Economic Association has some great resources for economics students who are interested in a PhD

• The AEA suggests:

  • 2 or 3 semesters of calculus
  • Linear algebra
  • Mathematical Statistics
  • Real Analysis

B.S. Requirements

• MAT 295: Calculus I
  • Overview: Analytic geometry, limits, derivatives, maxima-minima, related rates, graphs, differentials, exponential and logarithmic functions, mean-value theorem, L’Hospital’s rule, integration
  • Prerequisites: None
• MAT 296: Calculus II
  • Overview: Integration: the definite integral and applications; trigonometric functions, method of integration, improper integrals, infinite series, elementary differential equations, parametric equations, polar coordinates
  • Prerequisites: MAT 295
• ECN 505: Mathematical Economics
  • Overview:
  • Prerequisites:
• ECN 521: Economic Statsistics
  • Overview:
  • Prerequisites:
• ECN 522: Econometric Methods
  • Overview:
  • Prerequisites:

B.S. / M.A. Requirements

• ECN 505 (shared with B.S.)
• ECN 522 (shared with B.S.)
• ECN 601: Survey Microeconomic Theory
• ECN 602: Survey Macroeconomic Theory
• ECN 621: Econometrics I
• ECN 623: Econometrics III, Program Evaluation
• 12 credits of electives (500+ level)
  • At least 6 credits must be ECN courses
    • Ex: ECN 610 (Environmental and Natural Resource Economics), ECN 731 (Public Expenditures)
  • 6 credits can be from other departments (with permission from Dr.Horrace)
    • Ex: Courses with FIN, IST, MAS, MAT prefixes

Courses I've Taken

Below is a list of resources I found useful for developing the mathematical intuition required for economic research. These are in addition to the required courses listed in the program descriptions above.

Math

Calculus

• Overview: MAT 397: Calculus III
  • Analytic geometry and vectors; functions of more than one variable, multiple integrals, partial differentiation, physical applications, line and surface integrals of scalar functions and vector fields, Green’s, Stokes’, and divergence theorems
  • Prerequisites:

Linear Algebra

• MAT 331: Linear Algebra I

  • Overview: Linear equations, n-dimensional euclidean space, linear independence, bases, linear transformations, matrices and determinants, eigenvalues and eigenvectors.
  • Prerequisites:

• MAT 531: Linear Algebra II (Proof based)

  • Proofs for results from MAT 331, vector spaces over an arbitrary field, linear transformations, inner products
  • Prerequisites:

Analysis

• MAT 375: Introduction to Abstract Mathematics
  • Principles of symbolic logic, set theory, basic function theory, relations, and cardinality. Emphasis on developing proof-writing skills, including mathematical induction.
• MAT 412: Real Analysis I
  • Overview: Introduction to the foundations of calculus covering topics from the following: the real number system is a complete ordered field, sequences, limits, Bolzano-Weierstrass, Cauchy sequences, limits of functions, continuity, Extreme Value theorem, Intermediate Value theorem, nowhere continuous functions, uniform continuity. Differentiability of functions of one real variable, Mean value theorem, generalized mean value theorem, L’Hopital’s rule, Taylor’s theorem, Inverse function theorem.
  • Prerequisites:

Statistics

• MAT 651: Probability and Statistics I (currently taking)
  • Overview: This is the first course for math PhD students who want to specialize in statistics. Students from other departments may also enroll, but I'd recommend speaking to the professor first.
  • A review of basic probability theory, transformations and moments, common families of distributions, multiple random variables and multivariate transformations, conditional probability and hierarchical distributions, sampling from the normal distributions, convergence concepts, order statistics.
  • Prerequisites: MAT 295, 296, 397

Other Useful Options

These are other courses that I haven't taken, but frequently appear on PhD program admissions pages. The Math Department at SU lists all course syllabi dating back to 2018

Math

• MAT 414: Ordinary Differential Equations
• MAT 512: Real Analysis II
• MAT 521: Introduction to Probability
• MAT 525: Mathematical Statistics