Mathematics
Bridge to College Algebra
Credit: 1/2
Length: 1 semester
Prerequisites: Algebra 1 and Geometry
Fulfills: STEM elective
Concurrent Credit: None
Bridge to College Algebra is a course for first semester ASMSA students who need additional practice building the fundamental algebra skills needed for success in future ASMSA courses. Special attention is given to lines, linear equations, quadratic equations, linear inequalities, polynomial operations, rational expressions, radicals, and exponent operations.
Geometry
Credit: 1/2
Length: 1 semester
Prerequisites: Algebra 1
Fulfills: STEM elective
Concurrent Credit: None
ASMSA Geometry utilizes technology to investigate the traditional topics of Euclidean Geometry, including points, lines, planes, triangles, polygons, polyhedrons, circles, and spheres. Students will be expected to learn the basics of proof structure, and how to incorporate that structure into building a sound mathematical argument which will be communicated using LaTeX. Geometry is only available to sophomores.
College Algebra
Credit: 1
Length: 1 semester
Prerequisites: Algebra 2, Geometry, and ACT Math subscore of 19
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 1403 - College Algebra - 3 hours
College Algebra is an integrated course of study in mathematics as a prerequisite to calculus. Mathematical reasoning skills are emphasized as students are guided through an exploration of topics including functions, polynomials, exponents, matrices, systems of equations, and inequalities.
Trigonometry
Credit: 1
Length: 1 semester
Prerequisites: College Algebra(MATH 1403) and Geometry or by invitation of department chair
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 1453 - Plane Trigonometry - 3 hours
Trigonometry is a prerequisite course for calculus and emphasizes building the algebraic and mathematical reasoning skills needed for success in a calculus course. The six trigonometric functions are defined using the unit circle and right triangles. Identities and graphs associated with those functions and their inverses are investigated extensively. Additionally, the students will be guided through an investigation of complex numbers, vectors, and oblique triangles.
Pre-Calculus Mathematics
Credit: 1
Length: 1 semester
Prerequisites: College Algebra(MATH 1403) and Geometry or adequate placement score
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 1715 - Precalculus Mathematics - 5 hours
Designed for students in majors requiring MATH 2804 Calculus I, this course covers advanced topics from algebra specifically necessary for calculus and covers the concepts of plane trigonometry, emphasizing circular functions of real numbers. Emphasizes the creation and analysis of mathematical formulas to model physical situations. Concepts covered include polynomial, rational, exponential, logarithmic, and trigonometric functions and equations, inverse functions, complex numbers in rectangular and trigonometric form, systems of equations, matrices, determinants, triangles, identities, and vectors.
Calculus 1
Credit: 1
Length: 1 semester
Prerequisites: College Algebra (MATH 1403) and Trigonometry(MATH 1453), or Precalculus(MATH 1715), or qualifying placement scores
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 2804 - Calculus 1 - 4 hours
Calculus I focuses on the development of mathematical reasoning skills needed to investigate techniques involved in modeling change. Students are initially engaged in a study of limits. They are then shown how to use limits to define the derivative and the definite integral. Students build skill in using techniques of differentiation and its applications, and the Fundamental Theorem of Calculus.
Calculus 2
Credit: 1
Length: 1 semester
Prerequisites: Calculus 1(MATH 2804) with a minimum grade of C
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 2854 - Calculus 2 - 4 hours
Calculus 2 continues the exploration of calculus. Emphasis is placed on techniques of integration, infinite series, L′Hôpital’s Rule, polar coordinates, and parametric curves.
Calculus 3
Credit: 1
Length: 1 semester
Prerequisites: Calculus 2(MATH 2854) with a minimum grade of C
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 2904 - Calculus 3 - 4 hours
Calculus 3 continues the exploration of calculus into higher dimensions. Topics include partial derivatives, multiple integrals, and vector analysis.
Differential Equations
Credit: 1/2
Length: 1 semester
Prerequisites: Calculus 2(MATH 2854) with a minimum grade of C
Fulfills: STEM elective
Concurrent Credit: UAFS MATH 2914 - Differential Equations - 4 hour
Differential Equations is an advanced mathematics course introducing the concepts of differential equations as natural consequences of the scientific ideas of exponential growth and oscillatory motion and their solution dependent upon initial conditions. Equations are studied qualitatively to examine the behavior of solutions and make prediction. Equations are also studied quantitatively by developing techniques to obtained solutions to first and second order differential equations in closed form. Linear operators are introduced. The main applications are annuities, falling bodies with air resistance, chemical mixing, the mass-spring system and the pendulum. Euler's method for approximating solutions is also included.
Discrete Math
Credit: ½
Length: 1 Semester
Pre- or co-requisites: Calculus 1(MATH 2804)
Co-requisites: College Algebra or consent of department chair
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS MATH 2443 - Discrete Mathematics 1 - 3 hours
Discrete Mathematics is a one-semester course designed to teach proof development and logic. This course is intended for the student interested in advanced mathematics, computer science, and logic. The course provides an intensive study of logic and higher levels of mathematical proofs while emphasizing basic skills in abstract algebra, the logic of sets, relations, functions, algorithms, counting methods, graph theory and trees, and basic number theory.
Introduction to Statistical Methods
Credit: 1
Length: 1 semester
Prerequisites: Algebra 2, or College Algebra(MATH 1403), or adequate placement score
Fulfills: Concurrent Credit Core - Math
Concurrent Credit: UAFS STAT 2503 - Probabbility & Statistics 1 - 3 hours
Introduction to Statistical Methods is introduction to the fundamental ideas of statistics, including descriptive statistics, normal distributions, sampling experiments, statistical inference, and elementary probability.
BioStatistics - Listed under Biology
Linear Algebra
Credit: ½
Length: 1 Semester
Prerequisites: Calculus 1
Fulfills: STEM elective
Concurrent Credit: None
Linear Algebra is a one-semester course designed to teach elementary linear algebra and the application of linear algebra in solving systems of linear equations. Linear Algebra is intended for the student interested in advanced mathematics, either for applications in physics, computer science, or other applied fields, or as an introduction to theoretical mathematics. The course provides an introduction to mathematical proof while emphasizing the applications of linear algebra. The calculator and computer are used to facilitate the work on matrices and systems of linear equations and on any other topics deemed appropriate.
Number Theory
Credit: 1/2
Length: 1 semester
Prerequisites: College Algebra
Co-requisites: Calculus
Fulfills: STEM Elective
Concurrent Credit: None
Number Theory is a course designed to meet the needs of advanced students who are interested in a pure mathematics course. Number Theory topics include, but are not limited to, Chinese Remainder Theorem in the context of solving systems of equations, Diophantine equations in context, Cryptanalysis, the Euler phi function, Fermat’s Little Theorem, and special primes, i.e., Fermat and Mersenne primes. Students often have their first true experience with proof. Number Theory is offered pending faculty availability and student interest.
Cryptography
Credit: 1/2
Length: 1 semester
Prerequisites: College Algebra (MATH 1403), Discrete Math is recommended but not required
Fulfills: STEM elective
Concurrent Credit: none
Cryptography is the science of secret writing with the goal of protecting the meaning of a message. This course will be a hybrid math and computer science course. Topics include Substitution Ciphers, Block Ciphers, RSA cryptography, the Diffie-Hellman and Elgamal Encryption systems, and Elliptic Curve cryptography. The mathematical principles behind these encryption methods include topics from algebra, number theory, and abstract algebra. Students will learn the pertinent mathematics and how to write programs that encrypt and decrypt messages using the various encryption systems covered in the course.
Quantitative Reasoning
Credit: 1/2
Length: 1 semester
Prerequisites: Algebra 2
Fulfills: STEM elective
Concurrent Credit: None
Unlock the power of mathematics for everyday life with Quantitative Reasoning. This course offers a comprehensive exploration of mathematical concepts essential for navigating the modern world. From managing personal finances to understanding statistical trends, students will engage with topics such as financial planning, probability analysis, mathematical modeling, and measurement principles. Students will develop critical thinking skills and mathematical proficiency applicable across various disciplines. By emphasizing real-world applications, this course equips students with the quantitative literacy needed to succeed in an increasingly data-driven society.