Navigating the Mathematical Landscape at AAMU: A Comprehensive Undergraduate Bulletin

The academic journey at Alabama A&M University (AAMU) is meticulously designed to equip students with the foundational knowledge and advanced skills necessary for success in their chosen fields. Within this framework, the Department of Mathematics plays a pivotal role, offering a diverse array of courses catering to a broad spectrum of academic pursuits, from foundational arithmetic to sophisticated abstract algebra and statistical analysis. This bulletin provides a detailed overview of the undergraduate mathematics curriculum, outlining course objectives, prerequisites, and their relevance to various degree pathways. Understanding this landscape is crucial for all students, whether they are embarking on their collegiate careers or seeking to deepen their mathematical understanding.

Foundational Mathematics: Building Blocks for Success

For students entering AAMU, a solid mathematical foundation is paramount. The university offers a range of developmental and introductory courses designed to meet students at their current level of proficiency and guide them towards advanced studies.

Developmental Mathematics courses serve as the bedrock for those needing to strengthen their fundamental arithmetic, algebraic, and geometric skills. MTH 010 (Developmental Mathematics), previously known as MTH 100, is a 3-credit hour course that covers basic arithmetic, basic algebra, and basic geometry concepts, along with pertinent application problems. Successful completion of this course, often determined by a placement test, is a stepping stone toward fulfilling any degree requirement.

Building upon these fundamentals, MTH 011 (Fundamentals of Mathematics), formerly MTH 101, is another 3-credit hour offering. This course delves into mathematical problem-solving, equipping students with the skills to tackle a variety of mathematical challenges. Placement into MTH 011 may be based on the COMPASS assessment, ensuring students are enrolled in the most appropriate level for their needs.

For students requiring a more in-depth exploration of algebraic concepts, MTH 012 (Intermediate Algebra), formerly MTH 105, provides a comprehensive 3-credit hour curriculum. This course is designed to prepare students for higher-level mathematics, covering topics such as polynomial and rational functions, exponential and logarithmic functions, inverse functions, and both linear and non-linear systems of equations. Mastery of Intermediate Algebra is often a prerequisite for MTH 125 (Calculus I), which is the initial course in the calculus sequence for many STEM-oriented curricula.

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MTH 013 (Modern Mathematics), a 3-credit hour course previously designated as MTH 107, offers a contemporary perspective on mathematical concepts. It explores fundamental principles of logic, sets, and functions, providing students with a broader appreciation for the structure and application of mathematics.

Quantitative Reasoning and Non-STEM Pathways

Recognizing that not all students will pursue STEM fields, AAMU offers specialized courses designed to foster quantitative literacy and analytical skills essential for a wide range of disciplines.

MTH 108 (Quantitative Reasoning) is a 3-credit hour course designed for students in non-STEM fields. This course emphasizes the practical application of mathematics, integrating concepts from algebra, probability, and statistics. The curriculum is structured to ensure that mathematical reasoning is embedded throughout the course, making it highly relevant to diverse fields of study. For students whose chosen field of study is a NON-STEM mathematical pathway, MTH 108 provides a robust foundation. Depending on the specific requirements of their major, additional mathematics coursework may be required.

Complementing the theoretical aspects, MTH 108E (Quantitative Reasoning with Lab) offers a 3-credit hour experience with 4 contact hours, including a dedicated lab component. This hands-on approach allows for deeper engagement with quantitative concepts, with mathematical reasoning embedded throughout the course. Similar to MTH 108, this course is ideal for students on a NON-STEM mathematical pathway. If their chosen pathway requires further mathematical depth, additional mathematics coursework may be necessary.

Bridging to Calculus and Advanced Topics

For students aspiring to pursue STEM disciplines or requiring a more rigorous mathematical background, a sequence of pre-calculus and calculus courses is available.

MTH 110 (Finite Mathematics), a 3-credit hour course, is specifically designed for students not majoring in science, engineering, commerce, or mathematics. This course introduces fundamental concepts of discrete mathematics, including set theory, logic, combinatorics, and probability theory. It also explores topics such as matrices, determinants, and the simplex method for linear programming, providing valuable analytical tools for various applications.

MTH 111 (Elementary Statistics I), a 3-credit hour course, serves as an introduction to the principles and applications of statistics. It covers descriptive statistics, probability distributions (including binomial and normal distributions), estimation, and hypothesis testing. This course is particularly relevant for students on a pathway that requires statistical understanding, and additional mathematics coursework may be required depending on their specific major.

MTH 112 (Pre-Calculus Algebra), formerly MTH 103, is a 3-credit hour course essential for students preparing for calculus. It systematically covers topics such as polynomial, rational, exponential, and logarithmic functions; inequalities; systems of equations and inequalities; and the binomial theorem. Advanced topics may include matrices, Cramer’s rule, and mathematical induction, providing a comprehensive review and extension of algebraic concepts.

MTH 112E (Pre-Calculus Algebra with Lab) is a 4-credit hour offering that includes 3 clock hours of lecture and 1 clock hour of lab per week. This enhanced version provides additional practice and reinforcement of topics such as functions in two variables, variation, and functions, alongside inequalities and the binomial theorem. The lab component offers further exploration of matrices, Cramer’s rule, and mathematical induction, with dedicated time for hands-on activities. Students will engage in lab exercises each week as part of the course.

MTH 113 (Pre-Calculus Trigonometry), formerly MTH 104, is a 3-credit hour course focusing on the essential elements of trigonometry. It covers the analysis of trigonometric functions, trigonometric identities, and trigonometric equations. The course also extends to vectors, complex numbers, DeMoivre’s Theorem, and polar coordinates, providing a comprehensive understanding of trigonometric principles and their applications.

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For a consolidated preparation for calculus, MTH 115 (Pre-Calculus Algebra and Trigonometry) offers a 4-credit hour program that combines the essential elements of both MTH 112 and MTH 113. This integrated approach ensures students have a strong command of algebraic manipulation and trigonometric concepts, including the binomial theorem, preparing them thoroughly for the rigors of calculus.

The Calculus Sequence: Core of STEM Education

The calculus sequence at AAMU provides the fundamental tools for understanding change and accumulation, critical for students in science, engineering, and mathematics.

MTH 120 (Calculus and Its Applications) is a 3-credit hour course designed for students in commerce and business. It focuses on the applications of calculus in these fields, covering differential and integral calculus with relevant applications. It is important to note that this course does not substitute for the more rigorous MTH 125 or MTH 126.

MTH 125 (Calculus I), formerly MTH 171, is a foundational 4-credit hour course. It introduces the concepts of limits, derivatives, and integrals, with applications to area and related rates. This course is taken primarily by students in science, engineering, and mathematics majors, providing the essential groundwork for their respective disciplines.

Building upon Calculus I, MTH 126 (Calculus II), formerly MTH 172, is another 4-credit hour course that extends the study of calculus. Topics include advanced integration techniques, sequences and series, parametric equations, and polar coordinates. The course also covers applications of integration and introduces multivariable calculus concepts such as partial derivatives and lines and planes in space, forming a crucial part of the calculus sequence.

For students seeking an enriched and accelerated learning experience, MTH 145 (Calculus I Honors) and MTH 146 (Calculus II Honors) offer 4-credit hour counterparts to the standard calculus sequence. These honors courses delve deeper into the subject matter, often incorporating more challenging problems and an independent application project. They cover similar topics to their non-honors equivalents, including limits, derivatives, integrals, and applications to area in MTH 145, and advanced integration techniques, sequences, series, parametric equations, polar coordinates, and multivariable concepts like partial derivatives and planes in space in MTH 146. These courses are designed for highly motivated students and may involve a significant application project.

Advanced Mathematics and Specializations

Beyond the core calculus sequence, AAMU offers a rich curriculum in advanced mathematics, catering to students with specialized interests and those pursuing graduate studies.

MTH 200 (Mathematical Computations) is a 1-credit hour course designed to familiarize students with essential computational tools used in advanced mathematics. It often involves the use of software and techniques relevant to courses such as Algebra and Trigonometry, Calculus I and II, and Linear Algebra.

MTH 227 (Calculus III), formerly MTH 201, is a 4-credit hour course that extends the concepts of calculus to three dimensions. It covers vector calculus, including line integrals, surface integrals, Green’s Theorem, the Divergence Theorem, and Stoke’s Theorem, providing a comprehensive understanding of multivariable calculus.

MTH 235 (Mathematics for Elementary Teachers) is a 3-credit hour course specifically tailored for aspiring elementary educators. It focuses on the fundamental mathematical concepts and problem-solving strategies that teachers need to effectively instruct young learners. The course emphasizes number theory, geometry, measurement, and data interpretation, with the use of technology being an integral part of the learning process. This course is recommended for students pursuing a degree in Mathematics or Secondary Education Mathematics.

MTH 237 (Introduction to Linear Algebra), formerly MTH 203, is a 3-credit hour course that introduces the fundamental concepts of linear algebra. It covers vector spaces, linear transformations, matrices, determinants, eigenvalues, and eigenvectors, along with inner product spaces. The course also explores the applications of matrix theory in solving differential equations, providing a powerful tool for modeling various phenomena.

MTH 238 (Applied Differential Equations), formerly MTH 202, is a 3-credit hour course that focuses on the theory and application of differential equations. It covers first-order differential equations, linear differential equations of higher order, methods of undetermined coefficients, reduction of order, and variation of parameters. The course also addresses systems of differential equations, Laplace transforms, and applications to physical systems such as mechanical vibrations and chemical mixtures, and solving initial value problems with discontinuous inhomogeneous terms.

Upper-Division Mathematics and Theoretical Foundations

The upper-division mathematics curriculum at AAMU delves into more abstract and theoretical areas, preparing students for advanced research and specialized careers.

MTH 301 (Abstract Algebra I) is a 3-credit hour course that introduces the fundamental structures of abstract algebra. It covers groups, subgroups, cyclic groups, permutation groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphisms, and isomorphisms. The course also explores the concept of direct products.

MTH 302 (Abstract Algebra II) is a continuation of MTH 301, offering a 3-credit hour exploration of advanced algebraic structures. This course delves into rings, integral domains, fields, and polynomial extensions of fields, providing a deeper understanding of algebraic systems.

MTH 303 (PHY 303) (Methods of Mathematical Physics) is a 4-credit hour course that bridges the gap between mathematics and physics. It covers advanced mathematical techniques essential for solving problems in theoretical physics, including differential equations, integral equations, and special functions.

MTH 305 (Applied Mathematics) is a 3-credit hour course designed to equip students with mathematical tools for solving real-world problems. It focuses on the application of differential equations, numerical methods, and modeling techniques. The course emphasizes the use of technology, including mathematical software, to solve complex problems. This course is particularly relevant for students in applied fields, and it is recommended for Mathematics majors.

MTH 307 (Geometry) is a 3-credit hour course that explores various branches of geometry, including Euclidean, non-Euclidean, and projective geometry. It provides a rigorous treatment of geometric concepts and their underlying axioms, fostering spatial reasoning and abstract thinking. Note that this course is not open to Mathematics majors, suggesting its focus on broader applications or interdisciplinary interests.

Statistics and Data Analysis

AAMU's Department of Mathematics offers a robust sequence of statistics courses, equipping students with the skills to analyze and interpret data in an increasingly data-driven world.

MTH 111 (Elementary Statistics I) serves as the introductory course, as previously described.

MTH 324 (ST 324) (Elementary Statistics II), a 3-credit hour course, builds upon the foundation of Elementary Statistics I. It covers topics such as correlation and regression, goodness-of-fit tests, analysis of variance (ANOVA), and contingency tables. A significant aspect of this course involves interpreting results generated by statistical software packages like SAS, SPSS, and STATPAK.

MTH 327 (ST 327) (Applied Regression Analysis) is a 3-credit hour course that delves deeper into the techniques of regression analysis. It covers multiple linear regression, model building, analysis of variance, and computer-assisted data analysis, providing students with advanced tools for understanding relationships between variables.

MTH 344 (ST 344) (Design and Analysis of Experiments I), a 3-credit hour course, introduces the principles of experimental design. It covers the construction and analysis of experimental designs, including completely randomized designs, randomized block designs, Latin squares, and factorial designs, equipping students with the skills to conduct rigorous research.

MTH 355 (ST 355) (Applied Statistics) is a 3-credit hour course that provides practical applications of statistical methods. It covers descriptive statistics, probability, inferential statistics, and analysis of variance. This course includes laboratory activities, allowing students to apply statistical concepts using real-world data. It is particularly beneficial for students in fields such as medicine and pre-nursing, and it is also suitable for statistics minors.

MTH 453 (ST 453) (Probability and Statistics) is a 3-credit hour course that offers a more theoretical treatment of probability and statistics. It covers probability distributions, random variables, sampling distributions, estimation, hypothesis testing, and limit theorems, providing a strong theoretical foundation for statistical inference.

MTH 473 (ST 473) (Statistics) is a 3-credit hour course that serves as an introduction to the theory of statistics. It covers estimation, hypothesis testing, and nonparametric and distribution-free procedures, offering a comprehensive overview of statistical methodologies.

MTH 444 (ST 444) (Applied Time Series Analysis) is a 3-credit hour course focused on the analysis of data collected over time. It covers stationary and non-stationary processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) models. The course delves into estimation in MA, AR, ARMA, and ARIMA processes, and emphasizes methodology, computer-aided modeling, and applications.

Theoretical Mathematics and Pure Mathematics

For students with a strong inclination towards theoretical mathematics, AAMU offers advanced courses in analysis, number theory, and abstract structures.

MTH 351 (Introduction to Real Analysis I) is a 3-credit hour course that provides a rigorous foundation in real analysis. It covers the logic of proof, negation, contrapositive, sets, relations, and functions. The course then delves into the properties of real numbers, sequences, series, limits, continuity, and uniform continuity, laying the groundwork for advanced mathematical reasoning.

MTH 352 (Introduction to Real Analysis II) continues the rigorous exploration of real analysis over 3 credit hours. This course focuses on differentiation, integration, sequences and series of functions, uniform convergence, and power series, further developing students' analytical and proof-writing skills.

MTH 371 (Number Theory) is a 3-credit hour course that explores the properties and relationships of integers. It covers topics such as divisibility, prime numbers, congruences, Diophantine equations, and number-theoretic functions, providing a deep dive into the fascinating world of numbers.

MTH 383 (Numerical Analysis) is a 3-credit hour course that focuses on the development and analysis of algorithms for solving mathematical problems numerically. It covers topics such as root finding, interpolation, numerical differentiation and integration, and the solution of systems of linear equations and differential equations, along with approximation and error analysis.

MTH 452 (Complex Analysis) is a 3-credit hour course that extends the concepts of calculus to the complex plane. It covers analytic functions, Cauchy-Riemann equations, complex integration, Cauchy’s Theorem, Taylor and Laurent series, and the calculus of residues, providing powerful tools for solving a wide range of mathematical and physical problems.

MTH 454 (Advanced Calculus) is a 3-credit hour course that offers a more advanced perspective on calculus, covering topics such as Lebesgue integration, measure theory, and functional analysis. This course is designed for students seeking a deeper theoretical understanding of calculus and its extensions.

Specialized and Capstone Experiences

AAMU’s mathematics program culminates in specialized courses and capstone experiences that allow students to synthesize their knowledge and apply it to complex problems.

MTH 401 (History of Mathematics) is a 1-credit hour course that provides a historical perspective on the development of mathematical ideas and discoveries. It explores the contributions of key mathematicians and the evolution of mathematical thought across different cultures and eras.

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