Undergraduate Course Descriptions

MAUY.0914 Precalculus for Engineers
4 points. Offered every term.
Prerequisites:
Diagnostic exam.
Corequisites:
EXUY 1
Notes:
Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Description:
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.

MAUY.1002 The Art of Mathematics
2 points. Offered in the fall.
Prerequisites:
Only firstyear students are permitted to enroll in this introductory level course.
Description:
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.

MAUY.1022 Calculus 1B
2 points. Offered every term.
Prerequisites:
AP Credit or MAUY 1012 or MAUY 1054.
Corequisites:
EXUY 1
Description:
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.

MAUY.1024 Calculus I for Engineers
4 points. Offered every term.
Prerequisites:
Diagnostic Exam or MAUY 912 or MAUY 914 (with a grade of B or better).
Corequisites:
EXUY 1
Description:
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, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1054 Calculus I with Precalculus
4 points. Offered every term.
Prerequisites:
Diagnostic exam or MAUY 912 or MAUY 954 or equivalent.
Corequisites:
EXUY 1
Notes:
Course required only for specific Majors in place of MAUY 1024/1324.
Description:
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.

MAUY.1124 Calculus II for Engineers
4 points. Offered every term.
Prerequisites:
Prerequisites: MAUY 1022 or MAUY 1024 or MAUY 1322 (with a grade of B or better) or MAUY 1324 (with a grade of B or better).
Corequisites:
EXUY 1
Description:
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. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1132 Numerical Methods for Calculus
2 points. Offered in the fall and the spring.
Prerequisites:
AP credit or transfer credit for Calculus I and II or MAUY 1112 or (MAUY 1054 and MAUY 1154).
Corequisites:
EXUY 1
Description:
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.

MAUY.1154 Calculus II with Precalculus
4 points. Offered every term.
Prerequisites:
MAUY 1054.
Corequisites:
EXUY 1
Notes:
Course required only for specific Majors in place of MAUY 1124/1424.
Description:
This course covers the first and second derivatives, optimization problems, antiderivatives, Fundamental Theorem of Calculus, techniques of integration, logarithmic, exponential and trigonometric 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.

MAUY.1324 Integrated Calculus I for Engineers
4 points. Offered every term.
Prerequisites:
Prerequisites: Diagnostic Exam or MAUY 912 or MAUY 914.
Corequisites:
EXUY 1
Description:
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, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1424 Integrated Calculus II for Engineers
4 points. Offered every term.
Prerequisites:
MAUY 1022 or MAUY 1024 or MAUY 1324.
Corequisites:
EXUY 1
Description:
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. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.2034 Linear Algebra and Differential Equations
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1132 or MAUY 1424.
Notes:
Not open to students who have taken MAUY 3044 or MAUY 3054.
Description:
MAUY 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.

MAUY.2054 Applied Business Data Analysis I
4 points. Offered in the fall and the spring.
Prerequisites:
MAUY 1054 or equivalent.
Notes:
Course required only for Management Majors. Credit for this course may not be used to satisfy the requirements for other majors.
Description:
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 decisionmaking. Applications to advanced statistical applications in business management. Emphasis is on application of concepts. Use of statistical software integrated with the previous topics.

MAUY.2114 Calculus III: MultiDimensional Calculus
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1132 or MAUY 1424.
Description:
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.

MAUY.2224 Data Analysis
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1132 or MAUY 1424.
Notes:
Not open to students who have taken MAUY 2233 or MAUY 3012 or MAUY 3022.
Description:
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 distributions of sample mean and sample variance; normal, t, and Chisquare distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.

MAUY.2233 Introduction to Probability
Identical to EEUY 2233.
3 points. Offered every term.
Prerequisites:
MAUY 109 or MAUY 2112 or MAUY 2114.
Notes:
Not open to students who have taken MAUY 2224 or MAUY 3012 or MAUY 3022.
Description:
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.

MAUY.2314 Discrete Mathematics
4 points. Offered in the fall and the spring.
Prerequisites:
Math Diagnostic Exam or MAUY 912 or MAUY 914 (minimum calculus level required). Prerequisite for Shanghai students: MATHSHU 110.
Notes:
This course and CSGY 6003 cannot both be taken for credit.
Description:
Logic, proofs, set theory, functions, relations, asymptotic notation, recurrences, modeling computation, graph theory.

MAUY.2414 Basic Practice of Statistics
4 points. Offered in the fall and the spring.
Prerequisites:
None.
Notes:
This course does not count towards degree if student has already taken MAUY 2224 or MAUY 2054.
Description:
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.

MAUY.3014 Applied Probability
Identical to MATHUA 233 Theory of Probability.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in MAUY 2114 and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2224, MAUY 2233/EEUY 2233, or MAUY 3022.
Description:
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.

MAUY.3022 Probability II
2 points. Offered in the fall and the spring.
Prerequisites:
MAUY 2224 or MAUY 3012.
Notes:
Not open to students who have taken MAUY 2233.
Description:
This course covers multivariate random variables, moment generating functions, properties of expectation, limit theorems and gives an introduction to random processes and their applications.

MAUY.3034 Applied Linear Algebra
4 points.
Prerequisites:
MAUY 1024 or MAUY 1324
Description:
Systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and least squares fit, singular value decompositions, computational techniques, conditioning, pseudoinverses.

MAUY.3044 Linear Algebra
Identical to MATHUA 140.
4 points. Offered every term.
Prerequisites:
A grade of C or better in MAUY 1022 or MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken MAUY 1533, MAUY 2034, MAUY 3054, or MAUY 3113.
Description:
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.

MAUY.3054 Honors Linear Algebra
Identical to MATHUA 148.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of A or better in MAUY 1022 or MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken MAUY 1533, MAUY 2034, MAUY 3044, or MAUY 3113.
Description:
This honors section of Linear Algebra is intended for wellprepared students who have already developed some mathematical maturity. Its scope will include the usual Linear Algebra (MAUY 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.

MAUY.3113 Advanced Linear Algebra and Complex Variables
3 points. Offered in the fall and the spring.
Prerequisites:
(MAUY 2114 or MAUY 2122) and (MAUY 2012 or MAUY 2034).
Notes:
Not open to students who have taken MAUY 1533, MAUY 3112, or MAUY 4433.
Description:
This course provides a deeper understanding of topics introduced in MAUY 2012 and MAUY 2034 and continues the development of those topics, while also covering functions of a Complex Variable. Topics covered include: The GramSchmidt process, inner product spaces and applications, singular value decomposition, LU decomposition. Derivatives and CauchyRiemann equations, integrals and Cauchy integral theorem. Power and Laurent Series, residue theory.

MAUY.3914 Project in Mathematics I
4 points. Offered in the fall and the spring.
Prerequisites:
Approval of departmental adviser.
Notes:
This course is repeatable for credit, but does not allow multiple enrollment in the same term.
Description:
In this course, students read, study, and investigate selected topics in mathematics.
Problems are discussed and presented by participating students. 
MAUY.4014 Theory of Numbers
Identical to MATHUA 248.
4 points. Offered in the fall.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1132 or MAUY 1424.
Description:
Divisibility and prime numbers. Linear and quadratic congruences. The classical numbertheoretic functions. Continued fractions. Diophantine equations.

MAUY.4044 Algebra
Identical to MATHUA 343.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in MAUY 4613 and (MAUY 3044 or MAUY 3054 or MAUY 3113), or permission of instructor.
Notes:
Cannot receive credit for both MAUY 4044 and MAUY 4054.
Description:
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.

MAUY.4054 Honors Algebra I
Identical to MATHUA 348.
4 points. Offered in the fall.
Prerequisites:
A grade of B or better in MAUY 4613 and (MAUY 3044 or MAUY 3054 or MAUY 3113) or instructor permission.
Notes:
Cannot receive credit for both MAUY 4044 and MAUY 4054.
Description:
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.

MAUY.4064 Honors Algebra II
Identical to MATHUA 349.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 4054 or (a grade of A in MAUY 4044 and instructor permission).
Description:
Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals.

MAUY.4114 Applied Statistics
4 points.
Prerequisites:
MAUY 2233 or MAUY 3014
Description:
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; chisquare, 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.
Notes:
Not open to students who have taken MAUY 2224

MAUY.4204 Ordinary Differential Equations
Identical to MATHUA 262.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in MAUY 2114 and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Notes:
Not open to students who have taken MAUY 2034 or MAUY 3083.
Description:
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: firstorder equations including integrating factors; secondorder equations including variation of parameters; series solutions; elementary numerical methods including Euler's methods, RungeKutta methods, and error analysis; Laplace transforms; systems of linear equations; boundaryvalue 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.

MAUY.4214 Applied Ordinary Differential Equations
4 points.
Prerequisites:
MAUY 2114 and (MAUY 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2034 or MAUY 4204.
Description:
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: firstorder equations including integrating factors; secondorder equations including variation of parameters; series solutions; elementary numerical methods including Euler's methods, RungeKutta methods, and error analysis; Laplace transforms; systems of linear equations; boundaryvalue 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.

MAUY.4314 Combinatorics
Identical to MATHUA 240.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1132 or MAUY 1424.
Description:
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 graphtheoretic problems.

MAUY.4324 Mathematics of Finance
Identical to MATHUA 250.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C+ or better in MAUY 2114 and a grade of C+ or better in (MAUY 2054 or MAUY 2224 or MAUY 2233 or MAUY 2414 or MAUY 3014 or MAUY 3022 or MAUY 4114).
Description:
Introduction to the mathematics of finance. Topics include: Linear programming with application pricing and quadratic. Interest rates and present value. Basic probability: random walks, central limit theorem, Brownian motion, lognormal model of stock prices. BlackScholes theory of options. Dynamic programming with application to portfolio optimization.

MAUY.4413 Applied Partial Differential Equations
3 points. Offered in the fall.
Prerequisites:
MAUY 2114 and (MAUY 3083 or MAUY 4204).
Description:
Modeling of physical processes. Classification of equations. Formulation and treatment of boundary and initialvalue problems. Green’s functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear firstorder equations and characteristics. D’Alembert solution of wave equation. Conservation laws and shock waves.

MAUY.4424 Numerical Analysis
Identical to MATHUA 252 Numerical Analysis.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in MAUY 2114 and (MAUY 3034 or MAUY 3044 or MAUY 3054 or MAUY 3113).
Description:
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 rootfinding procedures to differential equations and the finite element method.

MAUY.4434 Applied Complex Variables
4 points.
Prerequisites:
MAUY 2114 and (MAUY 2034 or MAUY 3034 or MAUY 3044 or MAUY 3054)
Notes:
Not open to students who have taken MAUY 3113.
Description:
A first course in complex analysis, with a focus on applications. Topics to be covered include the complex plane, analytic functions, complex differentiation, the CauchyRiemann equations, branch cuts, contour integration, the residue theorem, conformal mapping, applications to potential theory and fluid flow.

MAUY.4444 Intro to Math Modeling
Identical to MATHUA 251.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in MAUY 2114.
Notes:
Not open to students who have taken MAUY 2393.
Description:
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.

MAUY.4474 Chaos and Dynamical Systems
Identical to MATHUA 264.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in (MAUY 1124 or MAUY 1132 or MAUY 1424) and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Description:
Topics will include dynamics of maps and of first order and secondorder 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 onevariable 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).

MAUY.4613 Analysis I
3 points. Offered in the fall.
Prerequisites:
(MAUY 2114 or MAUY 2122) and (MAUY 2034 or MAUY 2132).
Description:
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.

MAUY.4614 Applied Analysis
4 points.
Prerequisites:
MAUY 2114 and (MAUY 2034 or MAUY 3034 or MAUY 3044 or MAUY 3054).
Description:
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.

MAUY.4623 Analysis II
3 points. Offered in the spring.
Prerequisites:
MAUY 4613.
Description:
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, RiemannStieltjes integral, uniform and absolute convergence of integrals, sequences, series, uniform convergence, Beta and Gamma functions.

MAUY.4634 Vector Analysis
Identical to MATHUA 224.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 4613.
Description:
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.

MAUY.4674 Differential Geometry
Identical to MATHUA 377.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 2114 and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Notes:
Not open to students who have taken MAUY 3303.
Description:
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 GaussBonnet Theorem.

MAUY.492X Independent Study
14 points. Offered in fall and spring.
Prerequisites:
Departmental adviser’s approval.
Notes:
This course is repeatable for credit.
Description:
In this course, students read, study and investigate selected topics in mathematics. Students discuss and present problems.

MAUY.4993 B.S. Thesis in Mathematics
3 points. Offered periodically.
Prerequisites:
Departmental adviser’s approval.
Description:
This 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 indepth knowledge of that area of Mathematics and proficiency in using its specific methods.