Online Pre-College Programs and Courses

An Introduction to Mathematical Cryptography is an introduction to modern cryptography with an emphasis on the mathematics behind the theory of public key cryptosystems and digital signature schemes. The course develops the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Other topics central to mathematical cryptography covered are classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures. Fundamental mathematical tools for cryptography studied include primality testing, factorization algorithms, probability theory, information theory, and collision algorithms. A survey of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography are included as well. This course is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course follows the actuarial Exam P syllabus and learning objectives to prepare students to pass the SOA/CAS Probability Exam. Topics include axioms of probability, discrete and continuous random variables, conditional probability, Bayes’ theorem, Chebyshev's Theorem, Central Limit Theorem, univariate and joint distributions and expectations, loss frequency, loss severity and other risk management concepts. Exam P learning objectives and learning outcomes are emphasized.

Prerequisite: Calculus II.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course will provide a practical introduction to mathematical proofs with the aim of developing fluency in the language of mathematics, which itself is often described as “the language of the universe.” Along with a library of proof techniques, we shall tour propositional logic, set theory, cardinal arithmetic, and metric topology and explore “proof relevant” mathematics by interacting with a computer proof assistant. This course on the construction of mathematical proof will conclude with a deconstruction of mathematical proof, interrogating the extent to which proof serves as a means to discover universal truths and assessing the mechanisms by which the mathematical community achieves consensus regarding whether a claimed result has been proven.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations.

Prerequisite: Grade of C- or better in AS.110.107 (Calculus II For Biological and Social Science) or AS.110.109 (Calculus II For Physical Sciences and Engineering) or AS.110.113 (Honors Single Variable Calculus) or AS.110.202 (Calculus II) or AS.110.302 (Differential Equations and Applications), or a 5 on the AP BC exam.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course is designed for students of all backgrounds to provide a solid foundation in the underlying mathematical, programming, and statistical theory of data analysis. In today's data driven world, data literacy is an increasingly important skill to master. To this end, the course will motivate the fundamental concepts used in this growing field. While discussing the general theory behind common methods of data science there will be numerous applications to real world data sets. In particular, the course will use Python libraries to create, import, and analyze data sets. 

Prerequisites: There are no mathematical prerequisites for this course although prior knowledge of calculus, statistics and/or programming can be helpful.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

Is the mind identical to the brain? Is the mind (or brain) a computer? Could a computer reason, have emotions, or be morally responsible? This course examines such questions philosophically and historically. Topics include the history of AI research from 1940s to present; debates in cognitive science related to AI (computationalism, connectionism, and 4E cognition); and AI ethics.

This course is scheduled to run Monday, Wednesday, and Friday between 10 a.m. and 11:30 a.m.

This online course is primarily delivered asynchronously; however, students must attend a 90-minue online discussion session each Monday, Wednesday, and Friday from 10:00 AM to 11:30 AM . Your instructor may schedule additional live interactions as well. Please refer to your syllabus for these opportunities and for important course deadlines.

Population genomics is the study of the structure, function, and variability of the entire genetic complement of organisms considered on a population scale. By examining how gene variants change in structure and frequency in populations over time, we can study the process of evolution and how it contributes to biodiversity and the formation of new species; this information can be used to increase the efficacy of conservation efforts. By studying gene variants underlying diseases at the scale of populations, we can better diagnose complex polygenic diseases like cancer. This course introduces the fundamentals of population genomics and provides an overview of the subfields of evolutionary genomics, conservation genomics, and medical genomics.

This self-paced program is primarily delivered asynchronously; however, your instructor may schedule live interactions as well. Please refer to your syllabus for these opportunities and for your important program deadlines.

Prerequisite: At least one semester of high school biology is recommended, but not required.

Required Text: There are no required textbooks for this program; all readings and resources will be made available to you throughout the program.

This course provides students with the background necessary for the study of calculus. It begins with a review of the coordinate plane, linear equations, and inequalities, and moves purposefully into the study of functions. Students will explore the nature of graphs and deepen their understanding of polynomial, rational, trigonometric, exponential, and logarithmic functions, and will be introduced to complex numbers, parametric equations, and the difference quotient.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses and may be taken as an Introduction to Proofs (IP) course. Topics include the formal properties of real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration. 

Prerequisite: Grade of C- or better in AS.110.201 (Linear Algebra) or AS.110.212 (Honors Linear Algebra), AND 110.202 (Calculus III) or 110.211 (Honors Multivariable Calculus).

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course continues AS.110.405 (Real Analysis I) with an emphasis on the fundamental notions of modern analysis. Sequences and series of functions, Fourier series, equicontinuity and the Arzela-Ascoli theorem, the Stone-Weierstrass theorem, functions of several variables, the inverse and implicit function theorems, introduction to the Lebesgue integral.

Prerequisite: AS.110.405 (Real Anaylsis I) or AS.110.415 (Honors Analysis I).

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

This course provides a fresh look at one of the most critical periods in the history of science – the so-called ‘Scientific Revolution’, spanning a period from approximately 1550 to 1750 – through the lens of colonial studies. It will address classic topics within the history and philosophy of science, such as the rise of observational epistemologies and the globalization of scientific knowledge. By connecting these philosophical concepts to the colonial contexts in which they arose, it will use tools from social history, economic history, and art history. Ultimately, it seeks not only to enrich students’ perspectives on the history of science, but also to inspire them to think about the connections between science and society across time, including in our own moment.

This course is scheduled to run Monday, Wednesday, and Friday between 9 a.m. and 11:30 a.m.

This course is designed for students of all backgrounds to provide a mathematical introduction to social choice theory, weighted voting systems, apportionment methods, and gerrymandering. In the search for ideal ways to make certain kinds of political decisions, a lot of wasted effort could be averted if mathematics could determine that finding such an ideal were actually possible in the first place. The course will analyze data from recent US elections as well as provide historical context to modern discussions in politics, culminating in a mathematical analysis of the US Electoral College. Case studies, future implications, and comparisons to other governing bodies outside the US are used to apply the theory of the course. Students will use Microsoft Excel to analyze data sets. There are no mathematical prerequisites for this course.

A flexible weekly schedule accommodates all student schedules and time zones, and courses include pre-recorded lectures, notes, and interactives to help students learn the material. Assessments include computer-scored items for immediate feedback as well as instructor-graded assignments for personalized learning. Students have access to instructors through email or individual reviews, and weekly instructor-led synchronous problem-solving sessions are recorded for viewing at any time. Students should expect to work a minimum of 5-10 hours per week.

A writing-intensive course (W) engages students in multiple writing projects, ranging from traditional papers to a wide variety of other forms, distributed throughout the term. Assignments include a mix of high and low stakes writing, meaning that students have the chance to write in informal, low-pressure--even ungraded--contexts, as well as producing larger, more formal writing assignments. Students engage in writing in the classroom through variety of means, including class discussions, workshop, faculty/TA lectures, and class materials (for instance, strong and weak examples of the assigned genre). Expectations are clearly conveyed through assignment descriptions, including the genre and audience of the assigned writing, and evaluative criteria. Students receive feedback on their writing, in written and/or verbal form, from faculty, TAs, and/or peers. Students have at least one opportunity to revise.