The main purpose of this course is to serve as a preparation for MATH 105, MATH 106, MATH 107, and MATH 112, with an emphasis on problem-solving techniques and graphing technology. Content includes the following topics: linear, quadratic, polynomial, rational, and absolute value equations and inequalities, algebraic expressions, graphing techniques, factoring techniques, exponents and basic data analysis. Students who wish to continue to higher level math courses will have the option to work with additional course material in algebra and trigonometry to facilitate this preparation. This course by itself cannot be used to satisfy the foundations math requirement for any degree program. Examinations are proctored.

This course will examine how the mathematics learned in high school is applied to real life situations. Topics may include personal finance, statistics, elections, symmetry, and scheduling. Some of the applications may be how the site of the Olympic Games is chosen, why spirals occur in nature, and how statistical data is collected and how it can be used to mislead the public. The course is designed for elementary education majors, fine arts majors, humanities majors, and those social and behavioral science majors whose further courses do not require College Algebra as a prerequisite. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

This course explores algebraic thinking from early childhood through middle school, with a focus on the different conceptions of algebra, including generalized arithmetic; patterns and functions; and modeling. Students will examine the different topics in K-8 algebra from an advanced perspective. Examinations are proctored.

The main purpose of this course is to help students understand, interpret, and represent data in a useful way to prepare students for courses in statistics. The course will provide students with the knowledge of basic mathematical and software tools and concepts which they can utilize to interpret quantitative information they encounter in their daily life. With the knowledge they gain, students will be able to better understand and assess the validity of quantitative information they receive through the web, newspaper, television, etc. Course topics will include creating various data summaries and descriptive statistics, probability, normal distributions, linear and other regression models, applying techniques to real world data sets. Examinations are proctored.

Topics include right triangle trigonometry, trigonometric functions and graphs, trig identities, inverse trig functions, law of sines, and law of cosines. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. Not applicable to the mathematics major or minor. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

Topics include properties of functions and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions with applications. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

Introductory topics in differential and integral calculus. Students are expected to have a graphing calculator. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

Introductory topics in differential and integral calculus, with particular emphasis on understanding the principal concepts and their applications to business. Microsoft Excel and graphing calculators will be used as tools for further understanding these concepts. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course.

A course using real examples developing and studying models of biological dynamical systems using concepts from calculus.

Review of algebra and trigonometry; study of functions including polynomial, rational, exponential, logarithmic and trigonometric. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. For students who have high school credit in college algebra and trigonometry but have not attained a sufficient score on the UA Math Placement Test to enter calculus. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

This is the first in a sequence of courses designed to lead to Calculus I. It serves a prerequisite for Math 121B. Topics covered include: functions and graphs, rates of change, transformations, inverse functions, quadratic and polynomial functions, rational functions, trigonometric functions. Examinations are proctored.

This is the second in a sequence of courses designed to lead to Calculus I. Topics covered include: trigonometric functions and identities, exponential and logarithmic functions and models, limits. Examinations are proctored.

Elementary functions, their properties, and uses in modeling. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used.

An introduction to first-semester calculus for engineering, science and math students, from rates of change to integration, with an emphasis on understanding, problem solving, and modeling. Topics covered include key concepts of derivative and definite integral, techniques of differentiation, and applications, using algebraic and transcendental functions. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. Examinations are proctored. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course.

An accelerated version of MATH 122B. Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

Continuation of MATH 122B or MATH 125. Techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics, and probability; differential equations from a numerical, graphical, and algebraic point of view; modeling using differential equations, approximations by Taylor series. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. Examinations are proctored.

Organizing data: displaying distributions, measures of center, measures of spread, scatterplots, correlation, regression, and their interpretation. Design of experiments: simple random samples and their sampling distribution, models from probability, normal distributions, and normal approximations. Statistical inference: confidence intervals and hypothesis testing, t procedures and chi-square tests. Not intended for those who plan further studies in statistics. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored.

This course is designed to introduce the mathematics teaching profession to mathematically talented college students. Students are given opportunities to observe and tutor in middle and high school mathematics classrooms. Additionally, class time will be dedicated to developing tutor techniques, examining learning styles, and exploring various methods of instruction. Readings, reflections, discussions, and group work will facilitate student understanding of the teaching and learning of mathematics. Students with a math placement level of calculus or higher will be given preference in the application process

This course is designed as a complement to MATH 116. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH 116. Concurrent registration in MATH 116 is required.

This course is designed as a complement to MATH 120R. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH 120R. Concurrent registration in MATH 120R is required.

This course is designed as a complement to MATH 122B. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH 122B.

This course is designed as a complement to MATH 129. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH129. Concurrent registration in MATH 129 is required.

This course is designed as a complement to Math 223. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in Math 223. Concurrent registration in Math 223 is required.

Truth-functional logic and quantification theory; deductive techniques and translation into symbolic notation.

Vectors, differential and integral calculus of several variables. Examinations are proctored.

Set theory, logic, discrete structures; induction and recursion; graphs and networks; techniques of proof. Examinations are proctored.

Solution methods for ordinary differential equations, qualitative techniques; includes matrix methods approach to systems of linear equations and series solutions. Examinations are proctored.

Organizing data; distributions, measures of center and spread, scatterplots, nonlinear models and transformations, correlation, regression. Design of experiments: models from probability, discrete and continuous random variables, normal distributions, sampling distributions, the central limit theorem. Statistical inference; confidence intervals and test of significance, t procedures, inference for count data, two-way tables and chi-square procedures, inference for regression, analysis of variance. Examinations are proctored.

With the annual Putnam mathematical competition as motivation, students engage weekly with challenging mathematics problems that require creativity, innovative thinking, and new insights to solve. This problem-solving lab thereby aims to help students synthesize and apply the theory, concepts, and techniques gained throughout their mathematics education in novel ways that lie outside the usual curricula of the major.

Development of a basis for understanding the common processes in elementary mathematics related to whole numbers, fractions, integers, and probability. This course is for elementary education majors only. Examinations are proctored.

Development of a basis for understanding the common processes in elementary mathematics related to estimation, graphing of functions, measurement, geometry, and data analysis. This course is for elementary education majors only. Examinations are proctored.

Applications and methods of linear algebra emphasizing matrices and systems of equations, determinants, eigenvectors and eigenvalues. This course is an excellent introduction to linear algebra for students who are interested in a math minor. It does not satisfy requirements for the math major. Students who might be interested in the math major should consider taking Math 313.

An algorithmic approach to solving systems of linear equations transitions into the study of vectors, vector spaces and dimension. Matrices are used to represent linear transformations and this leads to eigenvectors and eigenvalues. The precise use of definitions plays an important role. Examinations are proctored. This course is required in the math major and prepares students to take Math 323. It is a prerequisite to the majority of the higher level courses in mathematics.

Divisibility properties of integers, primes, congruencies, quadratic residues, number-theoretic functions.

Complex functions and integration, line and surface integrals, Fourier series, partial differential equations.

Elementary real analysis as an introduction to abstract mathematics and the use of mathematical language. Elementary logic and quantifiers; manipulations with sets, relations and functions, including images and pre-images; properties of the real numbers; supreme and infimum; other topics selected from cardinality, the topology of the real line, sequence and limits of sequences and functions; the emphasis throughout is on proving theorems.

Linear and nonlinear equations; basic solution techniques; qualitative and numerical methods; systems of equations; computer studies; applications drawn from physical, biological and social sciences.

Focusing on statistical inference, the course has two goals in addition to teaching the statistical techniques. One is theoretical: To explore the links between probability, statistics and calculus, showing students the mathematical underpinnings. The second is applied: Provides experience with real data sets, many bearing on education. Students who complete this course will be prepared to teach high school level statistics courses.

Focusing on statistical inference, the course has two goals in addition to teaching the statistical techniques. One is theoretical: To explore the links between probability, statistics and calculus, showing students the mathematical underpinnings. The second is applied: Provides experience with real data sets, many bearing on education. Students who complete this course will be prepared to teach high school level statistics courses.

In Introduction to Statistical Methods, we shall be using your background in biology and your previous knowledge of calculus and differential equations to consider the issues of collection, model derivation and analysis, interpretation, explanation, and presentation of data. Even though our examples derive mainly from the life sciences, statistics is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities.

This course will introduce statistical methods and training in statistical consulting aimed to analyze sports by using observational data on players and teams. With an emphasis on statistical inference and modeling, the students will learn how to analyze a sports related problem, utilize statistical tools to find a solution and interpret those results to sports professionals. The course will also offer the opportunity to focus on a semester long sports analytics project in partnership with a University of Arizona athletics team.

Basic computing skills including random variable generation, Monte Carlo integration, visualization, optimization techniques, re-sampling methods, Bayesian approaches, and introduction to statistical computing environments (R and Python). Material will provide hands-on experience with real world problems. It is expected that students have prior experience in a programming language, preferably Python.

Specialized work on an individual basis, consisting of instruction and practice in actual service to a department, program, or discipline.

This course is designed as a complement to Math 323. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in Math 323. The primary purpose of this course is to give students many opportunities to share their mathematical conjectures and their justifications to classmates. During class meetings students will debate the validity of mathematical statements and formal proofs. Concurrent registration in Math 323 is required.

Advanced propositional logic and quantification theory; metatheorems on consistency, independence, and completeness; set theory, number theory, and modal theory; recursive function theory and Goedel's incompleteness theorem.

Examination of secondary school mathematics curricula with emphasis on the development of math topics; study of assessment with emphasis on its alignment with instruction; and practicum experiences with emphasis on curriculum analysis and implementation of assessment measures.

Vector spaces, linear transformations and matrices, determinants, eigenvalues and diagonalization, bilinear forms, orthogonal and unitary transformations, Jordan canonical form.

A continuation of MATH 415A/515A. Topics may include finite groups, matrix groups, Galois theory, linear and multilinear algebra, finite fields and coding theory.

Applications of vector calculus, complex variables, and Sturm Liouville theory. Fourier series, Fourier and Laplace transforms, and separation of variables in classical partial differential equations. This course takes a more mathematical approach than Math 322.

Complex numbers, analytic functions, harmonic functions, elementary functions, complex integration, Cauchy's integral theorem, series representations for analytic functions,residue theory, conformal mapping, applications.

Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; inverse and implicit function theorems.

Set theory (countability/uncountability), topological spaces and continuous maps, metric spaces, connectedness and compactness, separability axioms and Hausdorff spaces, Tychonoff product theorem, introductory topics from algebraic topology (homotopy, fundamental group) or category theory.

[Taught Spring semester in odd-numbered years]. Divisibility properties of primes, congruences, quadratic residues, number-theoretic functions, primality, factoring, applications to crytopgraphy, introduction to algebraic numbers.

[Taught Spring semester in odd-numbered years]. Enumeration and construction of arrangements and designs; generating functions; principle of inclusion-exclusion; recurrence relations; a variety of applications.

General theory of initial value problems, linear systems and phase portraits, linearization of nonlinear systems, stability and bifurcation theory, an introduction to chaotic dynamics.

Properties of partial differential equations and techniques for their solution: Fourier methods, Green's functions, numerical methods.

Analysis of cash flows from an actuarial viewpoint. Interest theory, annuities, bonds, loans, and related fixed income portfolios, rate of return, yield, duration, immunization, and related concepts.

Analysis of cash flows from an actuarial viewpoint. Interest theory, annuities, bonds, loans, and related fixed income portfolios, rate of return, yield, duration, immunization, and related concepts.

Probability spaces, random variables, weak law of large numbers, central limit theorem, various discrete and continuous probability distributions.

Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods.

Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues.

Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues.

Numerical integration, solution of systems of ordinary differential equations, initial value and boundary value problems.

Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required.

Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of statistical mechanics; content varies

Advanced topics from modern mathematics. Content varies. The primary purpose of the course is to provide students the opportunity to gain knowledge, experience, and exposure to advanced topics in modern mathematics beyond what is presented in the core subjects for the math major.

Advanced propositional logic and quantification theory; metatheorems on consistency, independence, and completeness; set theory, number theory, and modal theory; recursive function theory and Goedel's incompleteness theorem. Graduate-level requirements include an in-depth research project on a central theme or topic of the course. Courses for which students receive the grade of P (Pass) do not satisfy requirements for the M.A. or Ph.D. or minor in philosophy.

Statistical concepts and methods applied to research in other scientific disciplines. Principles of estimation and hypothesis testing for standard one-and two-sample procedures. Correlation, linear regression. Contingency tables and analysis of variance.

Structure of groups, rings, modules, algebras; Galois theory.

Vector spaces, linear transformations and matrices, determinants, eigenvalues and diagonalization, bilinear forms, orthogonal and unitary transformations, Jordan canonical form. Graduate-level requirements include more extensive problem sets or advanced projects.

A continuation of MATH 415A/515A. Topics may include finite groups, matrix groups, Galois theory, linear and multilinear algebra, finite fields and coding theory. Graduate-level requirements include more extensive problem sets or advanced projects.

[Taught Spring semester in odd-numbered years] Selections from such topics as finite groups, abelian groups, characters and representations.

Advanced topics in algebraic number theory, analytic number theory, class fields, combinatorics; content varies.

[Taught Spring semester in odd-numbered years.] Rudiments of Riemann surfaces.

Applications of vector calculus, complex variables, and Sturm Liouville theory. Fourier series, Fourier and Laplace transforms, and separation of variables in classical partial differential equations. This course takes a more mathematical approach than Math 322. Graduate-level requirements include more extensive problem sets or advanced projects.

Lebesgue measure and integration, differentiation, Radon-Nikodym theorem, Lp spaces, applications.

Complex numbers, analytic functions, harmonic functions, elementary functions, complex integration, Cauchy's integral theorem, series representations for analytic functions,residue theory, conformal mapping, applications. Graduate-level requirements include more extensive problem sets or advanced project.

Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; inverse and implicit function theorems. Graduate-level requirements include more extensive problem sets or advanced projects.

Metric spaces, basic properties of normed linear spaces, distributions, the Lebesque intergral and Lebesque spaces, convergence theorems; applications chosen by the instructor.

Set theory (countability/uncountability), topological spaces and continuous maps, metric spaces, connectedness and compactness, separability axioms and Hausdorff spaces, Tychonoff product theorem, introductory topics from algebraic topology (homotopy, fundamental group) or category theory. Graduate-level requirements include additional assignments and/or projects.

Point set topology, the fundamental group, calculus on manifolds. Homology, de Rham cohomology, other topics. Examples will be emphasized.

[Taught Spring semester in odd-numbered years] Affine and projective varieties, morphisms and rational maps. Dimension, degree and smoothness. Basic coherent sheaf theory and Cech cohomology. Line bundles, Riemann-Roch theorem.

[Taught Spring semester in odd-numbered years]. Divisibility properties of primes, congruences, quadratic residues, number-theoretic functions, primality, factoring, applications to crytopgraphy, introduction to algebraic numbers. Graduate-level requirements include more extensive problem sets or advanced projects.

[Taught Spring semester in odd-numbered years]. Enumeration and construction of arrangements and designs; generating functions; principle of inclusion-exclusion; recurrence relations; a variety of applications. Graduate-level requirements include more extensive problem sets or advanced projects.

Properties of partial differential equations and techniques for their solution: Fourier methods, Green's functions, numerical methods. Graduate-level requirements include more extensive problem sets or advanced projects.

[Taught Spring semester in odd-numbered years]. Correspondence between Lie groups and Lie algebras, structure and representation theory, applications to topology and geometry of homogeneous spaces, applications to harmonic analysis.

[Taught Spring semester in odd-numbered years]. Stochastic Processes in continuous time: Levy processes, Martingales, Markov processes, introduction to stochastic integrals.

Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods.

Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues. Graduate-level requirements include more extensive problem sets or advanced projects.

Principles of designing experiments. Randomization, block designs, factorial experiments, response surface designs, repeated measures, analysis of contrasts, multiple comparisons, analysis of variance and covariance, variance components analysis.

Basic statistical principles and theory for modern machine learning, high dimensional data analysis, parametric and nonparametric methods, sparse analysis, shrinkage methods, variable selection, model assessment, model averaging, kernel methods, and unsupervised learning.

Error analysis, solution of linear systems and nonlinear equations, eigenvalue interpolation and approximation, numerical integration, initial and boundary value problems for ordinary differential equations, optimization.

[Taught Spring semester in odd-numbered years] Well-posedness, numerical boundary conditions, nonlinear instability, time-split algorithms, special methods for stiff and singular problems.

Advanced topics in asymptotics, numerical analysis, approximation theory, mathematical theory of mechanics, dynamical systems, differential equations and inequalities, mathematical theory of statistics; content varies.

Boundary value problems; Green's functions, distributions, Fourier transforms, the classical partial differential equations (Laplace, heat, wave) of mathematical physics. Linear operators, spectral theory, integral equations, Fredholm theory.

Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required. Graduate-level requirements include more advanced projects.

In-depth treatment of several contemporary problems or problem areas from a variety of fields, but all involving mathematical modeling and analysis; content varies.

[Taught Spring semester in odd-numbered years]. Regular and singular perturbations, boundary layer theory, multiscale and averaging methods for nonlinear waves and oscillators.

Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of statistical mechanics; content varies. Graduate-level requirements include additional assignments and/or projects.

The exchange of scholarly information and/or secondary research, usually in a small group setting. Instruction often includes lectures by several different persons. Research projects may or may not be required of course registrants.

The development and exchange of scholarly information, usually in a small group setting. The scope of work shall consist of research by course registrants, with the exchange of the results of such research through discussion, reports, and/or papers.

Introduction to research interests of the faculty. Required in Spring of first year in Ph.D. program in Mathematics and in the following Fall. Content varies.