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 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.

The main purpose of this course is to help students use algebraic and trigonometric functions to model real-life situations. Particular emphasis will be placed on applications relevant to Architecture and Speech, Language, and Hearing Sciences majors. Course topics will include ratios and proportions, functions and graphs, linear and quadratic functions and equations, trigonometric functions and equations, sinusoidal curve-fitting, exponential and logarithmic functions and equations, all with an emphasis on applications. 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. Students taking this course will learn how to interpret and develop calculus-based models of biological systems that describe how quantities change in realistic and relevant settings drawn from physiology, neuroscience, ecology and evolution. They will also learn the rudiments of a programing language sufficient to graph functions, plot data and simulate systems of differential equations. This course is intended for students in the biological sciences or those interested in pursuing a career in medicine and does not require any prior knowledge of calculus or of programming.

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.

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.

Seminar-style course designed to introduce math department majors to the mathematical community at large, support new majors as they adjust to university life and expectations, and build students' written and oral communication skills, especially on math-related topics.

Seminar-style course designed to introduce math department majors to the mathematical community at large, support new majors as they adjust to university life and expectations, and build students' written and oral communication skills, especially on math-related topics.

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 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.

Math 223 Vector Calculus (4 semester credit hours) The course covers differential and integral calculus of functions of several variables. Topics include vector valued and scalar functions, partial derivatives, directional derivatives, chain rule, local optimization, double and triple integrals, the line integral, Green's theorem, Stokes' theorem and the Divergence theorem. 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.

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.

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.

This course prepares students for working with linear systems that arise in engineering applications. Emphasis is placed on general principles of linearity and orthogonality. Topics include complex numbers and functions, matrix and vector algebra, linear systems of ODEs, Fourier series and transforms, separable 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.

An applications-oriented calculus-based statistics course with an introduction to statistical software. Course topics: Organizing data numerically and visually. Axioms of probability, conditional probability and independence. Random variables and expectation with emphasis on parametric families. Law of large numbers and central limit theorem. Estimation, bias and variance, confidence intervals. Hypothesis testing, significance and power. Likelihood ratio tests such as proportion tests, t-tests, chi-square tests, and analysis of variance.

An applications-oriented calculus-based statistics course with an introduction to statistical software. Course topics: Organizing data numerically and visually. Axioms of probability, conditional probability and independence. Random variables and expectation with emphasis on parametric families. Law of large numbers and central limit theorem. Estimation, bias and variance, confidence intervals. Hypothesis testing, significance and power. Likelihood ratio tests such as proportion tests, t-tests, chi-square tests, and analysis of variance.

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.

Individual research under the guidance of faculty.

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.

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 even-numbered years]. Introduction to cryptosystems and cryptanalysis. Basic number theory and finite fields. Basic complexity theory and probability. RSA and Diffie-Hellman protocols, factorization and discrete log attacks. Advanced encryption standard. Additional topics as times allows.

[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.

This course will focus on the mathematical modeling of fluid flows through and around organs and organisms, with an emphasis on topics of current medical and environmental interest. The natural world is replete with examples of cells, organs, and organisms whose shape influences flow to their benefit. For example, the shape of a maple seed generates lift which allows them to disperse farther. The design of the aortic valve prevents backflow during ventricular refilling while reducing disturbed regions of flow. The structure of a coral reef enhances the uptake of nutrients and the removal of wastes. A barracudas body shape reduces drag and allows it to quickly accelerate. In this course, we will mathematically describe the shape of organisms using 3D computer aided design (CAD). We will then use computational and experimental fluid dynamics to resolve the flow around 3D printed physical and numerical models. Mathematical topics will include the use of differential equations to describe fluid flow, numerical solutions of differential equations, image analysis, and the use of computational fluid dynamics software.

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

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.

A capstone experience that exposes students to the development, analysis, evaluation, and communication of statistical and data-scientific analyses for physical, biological, social, and other data-analytic problems.