Navigating the Mathematical Landscape at Angelo State University: A Comprehensive Syllabus Overview
Angelo State University offers a robust and diverse mathematics curriculum designed to cater to a wide array of academic pursuits, from foundational understanding to advanced specialization. This overview delves into the structure and content of the mathematics courses available, providing a detailed look at the progression of learning and the specific skills each course aims to impart. Whether a student is embarking on their higher education journey, preparing for a STEM-focused career, or seeking to fulfill requirements for teacher certification, the mathematics department at Angelo State provides a structured pathway to mathematical proficiency.
Foundational Mathematics: Building a Solid Base
The journey into mathematics at Angelo State often begins with courses designed to meet foundational requirements and address potential knowledge gaps. For students who have not yet met the Texas Success Initiative (TSI) requirements in mathematics, or those needing a refresher on fundamental concepts, the department offers a dedicated developmental option.
130C Developmental Mathematics (3-0) serves as an introductory course meticulously crafted to remediate identified deficiencies. This course provides a thorough review of fundamental operations in mathematics, aligning with the student’s mastery of the College and Career Readiness Standards. The curriculum may encompass elementary algebra and functions, intermediate algebra and functions, geometry and measurement, and data analysis, statistics, and probability, ensuring a comprehensive strengthening of essential mathematical skills before progressing to college-level coursework.
For students ready to commence their college-level mathematics, but who may not yet meet TSI standards, Angelo State provides a specialized pathway. The Course-based Option involves specially designated sections of freshman mathematics courses, identified as “T-sections” with section numbers beginning with a “T.” These sections are engineered to offer supplementary support for students who are not yet TSI complete. While these “T-sections” meet for six hours weekly, they are billed as three hours, impacting course load and Grade Point Average accordingly. Successfully completing a mathematics “T-section” not only fulfills the TSI requirements in mathematics but also grants credit for the corresponding college-level mathematics course, facilitating a seamless transition into degree programs. Students are strongly advised to consult with their academic advisor to select the appropriate course that aligns with their specific degree pathways.
Core Mathematics: Essential Skills for Diverse Disciplines
The core mathematics curriculum at Angelo State University is designed to equip students with essential analytical and problem-solving skills applicable across a multitude of disciplines. These courses provide the bedrock for more specialized studies and are often prerequisites for advanced coursework.
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1314/MATH 1314 College Algebra (3-0) offers an in-depth exploration and application of polynomial, rational, radical, exponential, and logarithmic functions, alongside systems of equations. This course may also incorporate additional topics such as sequences, series, probability, and conics, providing a broad foundation in algebraic concepts. A prerequisite for this course is the completion of Mathematics Texas Success Initiative (TSI) requirements.
Complementing College Algebra, 1316/MATH 1316 Trigonometry with Analytic Geometry (3-0) provides an in-depth study and application of trigonometry. Key areas include definitions, identities, inverse functions, solutions of equations, graphing, and the methods for solving triangles. Further topics such as vectors, polar coordinates, and parametric equations may also be explored. The prerequisite for Trigonometry with Analytic Geometry is either Mathematics 1314 or 1324, or a satisfactory score on a designated placement exam.
1324/MATH 1324 Finite Mathematics I (3-0) is tailored for students whose academic paths may involve applications in management, economics, and business. The course content includes basic algebra, linear equations, quadratic equations, functions and graphs, inequalities, logarithms and exponential functions, mathematics of finance, linear programming, matrices, and systems of linear equations. Similar to College Algebra, completion of Mathematics Texas Success Initiative (TSI) requirements is a prerequisite.
For non-STEM majors, 1332/MATH 1332 Introduction to Contemporary Mathematics (3-0) offers a more accessible approach to mathematical concepts. This course features introductory treatments of sets, financial mathematics, and probability and statistics, all presented with relevant applications. Emphasis is placed on embedding number sense, proportional reasoning, estimation, technology, and communication skills throughout the curriculum. Additional topics may also be covered, broadening the scope of contemporary mathematical thought. The prerequisite is the completion of Mathematics Texas Success Initiative (TSI) requirements.
1342/MATH 1342 Elementary Statistics (3-0) focuses on the crucial aspects of data handling: collection, analysis, presentation, and interpretation, along with an introduction to probability. The analytical components include descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing. The course strongly recommends the use of appropriate technology to enhance understanding and application. Completion of Mathematics Texas Success Initiative (TSI) requirements is a prerequisite for enrollment.
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Specialized Mathematics for Educators
Angelo State University recognizes the vital role of educators in shaping future generations and provides specialized mathematics courses designed to prepare elementary and middle school teachers. These courses go beyond rote memorization, focusing on conceptual understanding, pedagogical approaches, and the practical application of mathematical tools in the classroom.
1350/MATH 1350 Fundamental Mathematics for Elementary and Middle School Teachers (3-0) delves into the foundational elements of number systems. Topics include the system of whole numbers, numeration systems, the system of integers, elementary number theory, fractions and rational numbers, decimals and real numbers, and the properties of mathematical operations. A key feature of this course is its emphasis on in-class activities. Students engage in making and using math manipulatives, comparing different problem-solving techniques, fostering interdisciplinary connections, and experiencing mathematical concepts through auditory, visual, and kinesthetic approaches within inquiry-based activities. Completion of Mathematics Texas Success Initiative (TSI) requirements is a prerequisite.
1351/MATH 1351 Geometry for Elementary and Middle School Teachers (3-0) builds upon the foundational knowledge by exploring the fundamentals of plane and solid geometry. This includes a comprehensive study of measurement, area, volume, motion, and constructions. Similar to MATH 1350, this course incorporates hands-on learning experiences. In-class activities involve the creation and utilization of math manipulatives, the comparison of diverse problem-solving strategies, the establishment of interdisciplinary links, and the engagement with mathematical concepts through multi-sensory, inquiry-based approaches. The prerequisite for this course is Mathematics 1350.
1352 Algebraic Reasoning for Elementary and Middle School Teachers (3-0) focuses on the essential algebraic concepts relevant to teaching at the elementary and middle school levels. The curriculum covers ratio and proportion, elementary number theory, the fundamentals of algebra, statistics, and probability, with a strong emphasis on their application within the context of K-8 mathematics. This course also incorporates the pedagogical strategies highlighted in MATH 1350 and 1351, including the use of math manipulatives, exploration of problem-solving techniques, interdisciplinary connections, and multi-sensory, inquiry-based learning. Mathematics 1350 is a prerequisite for this course.
Advanced Mathematics: Preparing for STEM and Beyond
For students pursuing degrees in mathematics, computer science, engineering, or other STEM fields, Angelo State University offers a progression of advanced mathematics courses designed to build a strong theoretical and applied foundation. These courses introduce abstract concepts, rigorous proof techniques, and specialized areas of mathematics critical for advanced study and research.
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2305/MATH 2305 Discrete Mathematics I (3-0) is a pivotal course for students majoring in mathematics, computer science, and engineering. It is meticulously designed to cultivate abstraction, notation, and critical thinking skills essential for the mathematics most directly related to computer science. The course explores topics such as relations, functions, basic set theory, countability and counting arguments, mathematical induction, combinatorics, discrete probability, recursion, sequences and recurrence relations, elementary number theory, graph theory, and mathematical proof techniques. Completion of Mathematics Texas Success Initiative (TSI) requirements is a prerequisite.
2312/MATH 2312 Precalculus (3-0) serves as a comprehensive review and extension of algebraic concepts, preparing students for calculus. Topics include a review of algebra, solving equations and inequalities, a detailed study of functions and inverse functions, vectors in the plane and space, parametric equations, and lines and planes in space. A prerequisite of Mathematics 1314 or a suitable score on a placement exam is required.
2412/MATH 2412 Precalculus (4-0) offers a more intensive, combined study of algebra and trigonometry, along with other topics crucial for calculus readiness. This course provides a more accelerated pathway to calculus compared to MATH 2312. The prerequisite is Mathematics 1314 or a suitable score on a placement exam.
The calculus sequence begins with 2413/MATH 2413 Calculus I (4-0), which covers limits and continuity, the Fundamental Theorem of Calculus, the definition of the derivative of a function and techniques of differentiation, and applications of the derivative such as maximizing or minimizing a function. It also addresses the chain rule, mean value theorem, rate of change problems, curve sketching, and the definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculating areas. Prerequisites include Mathematics 1316 and 2312, or a suitable score on a placement exam.
2414/MATH 2414 Calculus II (4-0) continues the calculus sequence by focusing on the integration of transcendental functions, parametric equations and polar coordinates, advanced techniques of integration, sequences and series, and improper integrals. The prerequisite is Mathematics 2413.
3415/MATH 3415 Calculus III (4-0) extends the study of calculus to multivariable functions. Topics include partial differentiation, multiple integrals, vector functions, line integrals, Green’s Theorem, and Stoke’s Theorem. The prerequisite is Mathematics 2414.
Bridging Theory and Application: Applied and Specialized Mathematics
Beyond the core calculus sequence, Angelo State University offers a variety of specialized courses that delve into applied mathematics and theoretical underpinnings, catering to specific interests and career aspirations.
2350 Applied Mathematics for AI (3-0) is a forward-thinking course designed to introduce students to the mathematical concepts that are critical for understanding and implementing Artificial Intelligence algorithms. The primary focus is on linear algebra, probability, and statistics, providing a strong foundation for those interested in the computational and data-driven aspects of AI. Prerequisites include Mathematics 2305 and 2312.
3300 Introduction to Abstract Mathematics (3-0) serves as a crucial bridge to higher-level abstract mathematics. This course emphasizes logic, set operations, equivalence relations, properties of the real number system, and the cardinality of sets. A significant component of the course is dedicated to developing the essential skills required to read and construct formal mathematical arguments, a cornerstone of advanced mathematical study. The prerequisite is Mathematics 2413.
3301 Linear Algebra (3-0) provides a thorough examination of the algebra and geometry of finite-dimensional vector spaces. Topics include determinants, linear transformations and matrices, and characteristic values and vectors of linear transformations. This course is fundamental for many areas of science, engineering, and computer science. The prerequisite is Mathematics 2413.
3305 Discrete Mathematics II (3-0) builds upon the foundations laid in Discrete Mathematics I, exploring advanced topics such as graphs, matrices, computational methods, and other discrete structures. This course is essential for students in computer science and related fields. The prerequisite is Mathematics 2305.
3307 Probability and Statistics (3-0) offers a rigorous exploration of mathematical models for random processes. Key concepts include probability spaces, random variables, dependence and independence, mean values and moments of random variables, density and distribution functions, and the laws of large numbers. Prerequisites are Mathematics 2305 and 3415.
3310 Introduction to Problem Solving (3-0) is specifically designed for students pursuing secondary teacher certification in mathematics. This course aims to enhance analytical skills through exposure to a wide array of problem-solving techniques, utilizing concepts from algebra, geometry, trigonometry, and other areas of precalculus mathematics. The course also incorporates applications of graphing calculators and instructional software. Prerequisites include Mathematics 1316, 2312, and 2413.
3321 Statistics (3-0) provides a comprehensive survey of statistical methods. The curriculum covers distributions, central tendency, variability, and inferential procedures for two or more populations, including one-way ANOVA, and inferential methods for regression and correlation. Prerequisites include Mathematics 1314, 1316, 1324, 1342, 2312, or 2413.
3324 Applied Mathematics for Engineering (3-0) focuses on the application of mathematical principles to the analysis of engineering problems, with a strong emphasis on linear algebra and ordinary differential equations (ODEs). Topics include mathematical modeling of engineering problems, separable ODEs, first-, second-, and higher-order linear constant coefficient ODEs, the characteristic equation of an ODE, non-homogeneous equations, matrix addition and multiplication, the solution of linear systems of equations, rank, determinant, and inverse of a matrix, eigenvalues and eigenvectors, and the solution to systems of ODEs by diagonalization. The course also introduces the use of scientific computing for solving differential equations and linear algebra problems. Prerequisites are Mathematics 2413 and 2414.
3335 Differential Equations (3-0) covers the solution of differential equations, emphasizing their geometric and physical applications. This course is crucial for many areas of science and engineering. The prerequisite is Mathematics 3415.
Advanced Theoretical and Research Opportunities
For students seeking a deep dive into the theoretical underpinnings of mathematics and opportunities for original research, Angelo State University offers advanced courses and research programs.
4301 Abstract Algebra (3-0) delves into elementary number theory, including integer congruences and modular arithmetic, equivalence relations, and basic topics in ring and group theory. This includes the fundamental homomorphism theorems and the structure and basic properties of fields. This course is essential for students pursuing advanced degrees in mathematics. The prerequisite is Mathematics 3300.
4311 Numerical Analysis (3-0) explores the computational aspects of mathematics. Topics include number representations, error analysis, finding roots of equations, numerical integration, approximation, and differentiation, solving systems of equations, approximation by spline functions, numerical methods for ordinary differential equations, and Monte Carlo methods and simulation. Prerequisites are Mathematics 2414 and a strong background in calculus.
4321 College Geometry (3-0) offers a study of Euclidean, non-Euclidean, and transformational geometry, providing a broader perspective on geometric principles. The prerequisite is Mathematics 2413.
4322 A Survey of Mathematics with Applications (3-0) is a comprehensive course designed for students seeking a broad understanding of mathematical concepts and their applications, often within the context of teacher preparation. It covers logic and set theory, algebraic and transcendental functions, inverse functions, limits, the derivative and integral, sequences and series, linear systems, vectors, geometry, and probability and statistics. A significant emphasis is placed on applications utilizing the graphics calculator. This course has a set of rigorous prerequisites, including Mathematics 1316, 2305, 2312, 2413, 3301, 3307 or 3321, 3310, and 4321, along with a minimum GPA and admission to the Educator Preparation Program.
4331 Analysis (3-0) provides a rigorous treatment of fundamental concepts in real analysis. Topics include the real number system, functions, limits, continuity, differentiation, Riemann integration, and sequences. This course is crucial for advanced mathematical study. Prerequisites are Mathematics 2414 and 3300.
4335 Partial Differential Equations (3-0) offers a survey of partial differential equations (PDEs), including their classification, qualitative features, methods of solution, and applications in various scientific and engineering disciplines. Prerequisites are Mathematics 3324 or 3335.
4351 Topology (3-0) introduces students to the fundamental concepts of topology, a branch of mathematics concerned with the properties of space that are preserved under continuous deformations. Topics include sets and functions, metric spaces, topological spaces, compactness, separation, connectedness, and approximation. The prerequisite is Mathematics 3300.
4355 Topics in Abstract Mathematics (3-0) allows for the exploration of selected advanced topics from areas such as number theory, field theory, or other branches of higher mathematics. The emphasis is on developing a deep understanding of mathematical proofs. This course may be repeated for credit when the topic varies, offering flexibility for specialized study. Consent of the instructor is required.
4361 Complex Variables (3-0) delves into the study of complex numbers, analytic functions, complex integration, power series, residues, conformal mapping, and their applications. This course is essential for many areas of physics, engineering, and advanced mathematics. The prerequisite is Mathematics 2414.
Research and Experiential Learning
Angelo State University actively encourages students to engage in research and gain practical experience.
1191 Research (Individual research problems) and 1391 Research (Individual research problems) offer opportunities for students to undertake independent research projects under faculty guidance. These can be repeated for a total of four credits for 1191 and are valuable for developing research skills and exploring specific mathematical interests.
4091 Research offers more extensive research opportunities, with students able to earn up to 12 credits, and may be repeated for credit. A prerequisite is the consent of the department chair, indicating a higher level of engagement and commitment.
4171, 4271, 4371 Internship provides supervised internship experiences with approved cooperating businesses or government agencies. These internships offer practical, hands-on duties directly related to the mathematical sciences, with grading on a pass/fail basis. These courses may be repeated for credit, allowing students to gain diverse practical experiences.
4181 Seminar in Mathematics (1-0) provides a platform for presentations and discussions on selected topics, fostering an exchange of ideas among mathematics majors and faculty. This seminar can be taken at most twice for credit, encouraging active participation in the mathematical community.
Commitment to a Safe and Inclusive Environment
Angelo State University is dedicated to fostering an educational, working, and living environment that is free from sex discrimination and all forms of sexual misconduct. The university prohibits discrimination based on sex, including pregnancy, and all types of Sexual Misconduct, which is defined broadly to encompass sex-based harassment, discrimination, and unwelcome sexual behavior. Students, faculty, staff, and visitors are encouraged to report any incidents involving sexual misconduct to the Office of Title IX Compliance and the Title IX Coordinator, Mrs. Jessica Gooch. It is important to note that, as faculty members at Angelo State, instructors are mandatory reporters and are required to report incidents involving sexual misconduct to the Title IX Coordinator.
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