Math

Math 1A and 1B helps students develop the concepts, skills and habits that form the foundation of high school mathematics. Many of the tools are algebraic, but almost all concepts are looked at in a variety of ways including geometric, numeric and verbal approaches. Basic arithmetic and algebraic operations are modeled with physical manipulatives, making a geometric and visual connection with these operations. Our goal is for students to integrate and connect these methods.

Principal topics:

• Linear equations and graphs
• Introduction to the graphical representation of a variety of functions: continuous, discontinuous, step, linear, quadratic, exponential
• Equation solving by several methods: graphical intersection, numerical (systematic guess and check), “cover-up,” algebraic symbol manipulation
• Number Sense
• The distributive rule and factoring

(1 credit total)

Math 2A and 2B is an integrated course where students explore concepts through hands-on materials to create geometric conjectures, to use the language of algebra to describe some of these relationships, and to write formal proofs. Various algebraic concepts, such as simplification of square roots and variation functions, are approached geometrically. Slope and measurement are used to introduce trigonometric ratios. Writing computer programs and using dynamic geometry to create designs and figures, students deepen their understanding of geometric relationships as they experience the logic of computers.

Principal topics:

• Angles, polygons, parallel lines, circles
• Linear functions and systems of equations
• Distance and the Pythagorean Theorem
• Construction and dynamic geometry with GeoGebra software
• Scaling, proportions and variation functions
• Similarity and congruence
• Computer programming in Snap! : scripts and variables
• Sine, cosine, tangent in the right triangle
• Transformations: isometries and dilations
• Simultaneous equations
• Quadratics
• Exponential functions

(1 credit total)

Math 3A and 3B continues and deepens our work with algebraic manipulation and graphical representation of functions as mathematical models. The practices developed in previous courses are expected to be in place so that the focus is on understanding concepts and demonstrating mastery. In particular, we expect fluency with algebraic symbols and notation. As the last course required for all students, Math 3 rounds out the basics of mathematical literacy, intensifies the challenge for students, and provides the foundation for upper level electives.

Principal topics:

• Unit Circle Trigonometry
• Logarithms
• Law of Sines and Cosines
• Arithmetic and geometric sequences and series
• Composition of functions and inverse functions
• Families of functions
• Construction
• Formal Proof
• Polar coordinates and vectors
• Complex numbers

(1 credit total)

Advanced Math Applications is appropriate for students who would benefit from more experience with, and a deeper understanding of, the key math concepts that are foundation for Functions and other upper level math and science courses. Key topics from Math 1, 2 and 3 are reviewed and extended. Emphasis is placed on numeric and algebraic fluency. The course is also appropriate for any students interested in the history of mathematics and its applications to science.

Principal topics:

• Ratio, proportion and scientific notation applied to astronomical and sub-atomic scales
• Applications of linear, exponential, variation, quadratic and trigonometric functions in science
• Review and extension of logarithms including a mastery of the laws of exponents
• Applications of triangle trigonometry
• Unit circle trigonometry and radians applied to mapping, astronomy and basic physics
• Logarithms and logarithmic scale
• Mathematical language and notation, algebraic thinking, solving equations and graphing

(1/2 credit)

Prerequisite: Math 3

UAS Analytic Geometry introduces complex topics at the precalculus level that are challenging and useful for advanced students, but not prerequisite for the standard calculus course. The daily problems can be more substantial than the standard work in the core curriculum. There is a focus on moving fluently back and forth from a variety of algebraic forms to graphing in different coordinate systems in two and three dimensions. Students build models, do constructions, and derive equations from definitions and general principles.

Central topics:

• Vectors in three dimensions
• Conic sections
• Polar coordinate equations and graphs
• Parametric equations and graphs

(1/2 credit)

Prerequisite: Math 3

UAS Calculus A and B seeks to provide students with a solid foundation for subsequent college level courses in mathematics and other disciplines. The course is focused on differentiation, integration and their relationship. The math concepts are enhanced by applications relating to geometry, physics, economics, ecology and medicine. Students are expected to take full responsibility for their learning by using the text and applying all the skills and content learned in previous courses. They are expected to navigate between graphical, numerical, analytical and verbal representations of problems and to use the graphing calculator appropriately.

Principal topics:

• Differentiation
• Limits
• Integration
• Graphical analysis
• Introduction to differential equations and slope fields.

(1 credit)

Prerequisite: Functions

Computer Science 1 is an introduction to programming concepts using Snap!, a computer language developed at UC Berkeley. Snap! makes it possible for students to program images, animation and interactions and learn about algorithms, data handling and other fundamentals of computer programming, in a visual context.

Principal topics:

• Variables and scoping
• Passing parameters, returning values
• Functions and modularity
• Looping and conditionals
• Data structures (lists)
• List mutability
• Abstract data types
• Introduction to recursion

Prerequisite: Math 2 (1/2 credit)

UAS Computer Science 2 focuses attention on the central idea of abstraction, makes heavy use of the idea of functions as data, and discusses relevant topics in Computer Science such as functions as data, complexity and graph theory. It will also focus on some of the “Big Ideas” of computing such as recursion, concurrency and the limitations of computing. 

Principal topics:

• Algorithms, both classic and heuristic
• Algorithm Complexity: constant, linear, quadratic, exponential and logarithmic run times
• Recursion
• Higher Order Functions and using functions as data
• Graphs: paths, cycles, cliques

Prerequisites: Math 3, Computer Science 1 or instructor approval (1/2 credit)

UAS Computer Science 3 continues the Computer Science sequence, focusing on more advanced principles of software engineering, data structures and algorithms, emphasizing computability and feasibility. Topics in computer science such as Game Theory and Machine Learning will be discussed. 

Principal topics:

• Fundamental dynamic data structures including linear lists, queues, trees, arrays and dictionaries
• Computational complexity of algorithms and the key difference between denotation, computability and feasibility
• The object-oriented programming paradigm and a class-based approach
• Basic ideas and techniques underlying the design of intelligent computer systems
• Differences between machine learning, deep learning and neural networks
• Decision trees, pruning, and graph algorithms

Prerequisite: UAS Computer Science 2 (1/2 credit)

Data Science is an interdisciplinary course using programming and mathematics to analyze and understand very large amounts of unstructured data. This course is an introduction to the foundations of data science from three perspectives: inferential thinking, computational thinking, and real-world relevance. Students will use programming to analyze real-world datasets and use data visualization to communicate information. They will also delve into the social and legal issues and impacts surrounding data science such as privacy and data ownership, ethics, bias, and the misuse and misinterpretation of data. The course assumes prior knowledge of computer programming (abstraction, iteration, data types) and focuses on critical concepts and skills in statistical inference, in conjunction with hands-on analysis of diverse real-world datasets, e.g., UC admissions by high school, COVID-19 cases in the world or penguins in Antarctica.

Principal topics:

• Creating and extending tables/table fundamentals: row manipulation, grouping and pivoting, joining
• Data visualization
• Randomness and simulations
• Testing and assessing models
• Machine learning, training dataset

(1/2 credit)

Prerequisite: Computer Science 1

Discrete Mathematics: Puzzles and Graphs is a survey course, covering many topics in mathematics that are relevant in today’s world. Students will be introduced to and study practical applications of graphs and networks, theories about numbers, and formal logic. They will also be exposed to more abstract concepts deriving from these topics.

Principal Topics:

• Simple graphs and trees, networks, paths and isomorphisms
• Graph coloring, planar graphs and polyhedra
• Theorems and conjectures about prime numbers and prime factorizations
• Divisibility, modular arithmetic and cryptography
• Truth tables, truth values and logic puzzles

(1/2 credit)

Prerequisite: Math 3

UAS Functions focuses on the topics needed for calculus. It is structured around functions as models of change, emphasizing that they can be grouped into families that model real-world phenomena. One goal of this course is to begin the transition toward more text-based college-level courses and more independent student learning. Students extend and deepen their knowledge and skills of the core curriculum (Math 1-3).

Principal topics:

• Functions: increased depth on composition, inverse and general fluency
• Functions: transformations, odd and even, limits and end behavior
• Trigonometric functions, equations and identities, radians
• e and natural logarithms
• Polynomial and rational functions

(1/2 credit)

Prerequisite: Math 3 (and in some cases, Advanced Math Applications)

UAS Infinity: Theory of Infinite Sets and Chaos Theory allows students to discuss ancient paradoxes about infinity, and learn how Georg Cantor resolved them. This discussion launches our most theoretical course. Infinity includes a strong emphasis on formal proof and an introduction to chaos theory and fractal geometry, two computer-centered branches of mathematics. Connections are made with literature and philosophy.

Principal topics:

• Introduction to set theory and infinite sets
• Different-sized infinities, transfinite numbers
• Cardinals and ordinals arithmetic
• Proof by contradiction, proof by induction
• Iteration and recursion
• Fibonacci numbers
• Dynamical systems and the Mandelbrot set

(1/2 credit)

Prerequisite: Math 3

Statistics & Probability is an elective that concentrates on the applications of mathematics to the social and life sciences. This course is appropriate both for students who intend to go on to calculus, as well as students who do not. Students apply concepts of counting, combinations and permutations to probability problems, and to the foundations of statistics. They use appropriate tools and techniques to interpret data. The course also includes the mathematics underlying the sampling techniques used by scientists and pollsters.

Principal topics:

• Use of software to demonstrate and interpret data
• Analyzing the association of two variables from graphs
• Use of least squares line to determine and evaluate models for data
• Pascal’s triangle and binomial distribution
• Simulations with dice and with software
• Sampling and sources of bias

(1/2 credit)

Prerequisite: Math 3

UAS Space: Group Theory is an advanced geometry course, which includes a thorough exploration of symmetry, including an introduction to group theory, and extends students’ geometric experiences into three and four dimensions. Many hands-on 3D building labs, creative projects and the reading of mathematical fiction illustrate the concepts.

Principal topics:

• Geometric transformations
• Symmetry groups, tessellation, Escher art projects
• Matrices
• Three-dimensional geometry, especially polyhedra
• Flatland and the fourth dimension
• Zome System construction kit
• Computer labs, using Cabri and Cabri 3D software.

(1/2 credit)

Prerequisite: Math 3