Summer Term Undergraduate Courses

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.

Do we all see colors the same way? How did so many "good" people support the Nazi party? Do crossword puzzles really stave off Alzheimer's Disease? This course tries to answer these questions and many others, providing a comprehensive overview of the scientific study of the mind. We'll explore topics such as perception, language, memory, decision-making, creativity, love, sex, art, politics, religion, dreams, drugs, brain damage and mental illness, grappling with deep and long-standing controversies along the way: differences between the sexes, the relationship between mind and brain, causes and consequences of racism, human uniqueness (or not) within the animal kingdom, nature vs. nurture, good and evil, consciousness. Appropriate for anyone wanting to know who and what we are as human beings (or who noticed that psychology is now on the MCAT).

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

Introduces students to basic sociological concepts and perspectives, and applies them to a variety of topics including family, work, and the dynamics of class, gender, and racial/ethnic inequalities in the United States and globally.

Topological spaces, connectedness, compactness, quotient spaces, metric spaces, function spaces. An introduction to algebraic topology: covering spaces, the fundamental group, and other topics as time permits.

Prerequisite: AS.110.202 (Calculus III) or AS.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.

The fundamental principles of chemistry, including atomic and molecular structure, bonding, elementary thermodynamics, equilibrium and acids and bases, are introduced in this course. Can be taken with Introductory Chemistry Laboratory – I unless lab has been previously completed. Note: Students taking this course and Laboratory 030.105 may not take any other courses in the summer sessions at the same time and should devote their full time to these subjects. High school physics and calculus are strongly recommended as prerequisites. First and second terms must be taken in sequence. Students not enrolled in college (unless they are rising freshmen) may not take this course.

Continuation of AS.030.101 emphasizing chemical kinetics, chemical bonding. Topics: energy levels and wave functions for particle-in-a-box and hydrogen atom and approximate wave functions for molecules including introduction to hybrid orbitals. Note: Students taking this course and Laboratory 030.105-106 may not take any other course in the summer sessions at the same time and should devote their full time to these subjects. High school physics and calculus are strongly recommended as prerequisites. First and second terms must be taken in sequence.

Prerequisite: AS.030.101 (Introductory Chemistry I). Students enrolled in AS.030.103 (Applied Chemical Equilibrium and Reactivity with Lab) may not enroll in or receive credit for AS.030.102.

Laboratory work includes quantitative analysis and the measurement of physical properties. Open only to those who are registered for or have successfully completed Introductory Chemistry 030.101.

Prerequisites: Students must have completed or be enrolled in AS.030.101 (Introductory Chemistry I) or EN.510.101 (Introduction to Materials Chemistry) in order to register for AS.030.105. Students must have completed Lab Safety training prior to registering for this class. To access the tutorial, login to myLearning and enter 458083 in the Search box to locate the appropriate module.

Laboratory work includes some quantitative analysis and the measurement of physical properties. Open only to those who are registered for or have completed Introductory Chemistry II (AS.030.102). Permission required for pre-college students.

Prerequisites: AS.030.105 (Introductory Chemistry Laboratory I) and AS.030.101 (Introductory Chemistry I) OR EN.510.101 (Introduction to Materials Chemistry). Students enrolled in AS.030.103 (Applied Chemical Equilibrium and Reactivity w/Lab) may not enroll in or receive credit for AS.030.106. Students must have completed Lab Safety training prior to registering for this class. To access the tutorial, login to myLearning and enter 458083 in the Search box to locate the appropriate module.

This course provides an introduction to the fundamental chemistry of carbon compounds. Topics include interrelationships of structure, physical properties, synthesis, and reactions and their mechanisms as well as a brief overview of bio-organic chemistry. Note: Students taking this course and the laboratory 030.105-106 may not take any other course in the summer sessions and should devote full time to these subjects. First and second terms must be taken in sequence. Prerequisite: Introductory Chemistry or the equivalent.

Prerequisite: AS.030.102 (Introductory Chemistry II) or AS.030.103 (Applied Equilibrium and Reactivity w/Lab) or EN.510.101 (Introduction to Materials Chemistry) or AS.030.204 (Chemical Structure and Bonding w/Lab).

Laboratory work includes fundamental laboratory techniques and preparation of representative organic compounds. Open only to those who are registered for or have completed Introductory Organic Chemistry. Note: This one-semester course is offered each term. Introductory Organic Chemistry I/II requires one semester of the laboratory.

Prerequisites: AS.030.205 (Introductory Organic Chemistry I), which can be taken concurrently with AS.305.225( Introductory Organic Chemistry Laboratory); AND AS.030.102 (Introductory Chemistry II) AND AS.030.106 (Introductory Chemistry Laboratory II) OR AS.030.103 (Applied Equilibrium and Relativity w/Lab). Students must have completed Lab Safety training prior to registering for this class. To access the tutorial, login to myLearning and enter 458083 in the Search box to locate the appropriate module.

Laboratory work includes fundamental laboratory techniques and preparation of representative organic compounds. Open only to those who are registered for or have completed Introductory Organic Chemistry. Note: This one-semester course is offered each term. Introductory Organic Chemistry I/II requires one semester of the laboratory.

Prerequisites: AS.030.205 (Introductory Organic Chemistry I), which can be taken concurrently with AS.305.225( Introductory Organic Chemistry Laboratory); AND AS.030.102 (Introductory Chemistry II) AND AS.030.106 (Introductory Chemistry Laboratory II) OR AS.030.103 (Applied Equilibrium and Relativity w/Lab). Students must have completed Lab Safety training prior to registering for this class. To access the tutorial, login to myLearning and enter 458083 in the Search box to locate the appropriate module.

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.

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

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

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.

Mathematics for Sustainability covers topics in measurement, probability, statistics, dynamics, and data analysis. In this course, students will analyze, visually represent, and interpret large, real data sets from a variety of government, corporate, and non-profit sources. Through local and global case studies, students will engage in the mathematics behind environmental sustainability issues and the debates centered on them. Topics include climate change, natural resource use, waste production, air and water pollution, water scarcity, and decreasing biodiversity. The software package R is used throughout the course.

Prerequisites: Comfort with algebraic expressions and functions. No prior experience in coding is required.

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.

This course is an introduction to the theory of functions of one complex variable. Its emphasis is on techniques and applications, and it serves as a basis for more advanced courses. Functions of a complex variable and their derivatives; power series and Laurent expansions; Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions.

Prerequisite: Grade of C- or better in AS.110.202 (Calculus III) or AS.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.

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.

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 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.

Continuation of AS.030.205 Organic Chemistry I with special emphasis on organic synthesis and related synthetic methods. Students may not simultaneously enroll for AS.030.212 and AS.030.206.

Prerequisite: AS.030.205 (Introductory Organic Chemistry I).

A workshop devoted to creating compelling short scripts based on personal experience. Analysis of screened films and collaborative development of student work will emphasize how unique worlds and world views can reflect a larger shared humanity. Short critical and creative written exercises, and a longer, creative final project.

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.

The course will review the growing field of positive psychology and will review the research on positive human attributes such as optimism, happiness, hope, resiliency, self-esteem, altruism, empathy, and forgiveness. This course will explore the research on how such positive attributes are developed and how they relate to psychological and physical well-being.

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 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.

Probability and its applications, at the calculus level. Emphasis on techniques of application and on rigorous mathematical demonstration. Probability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, covariance and correlation, limit theorems. Students initiating graduate work in probability or statistics should enroll in EN.553.620 or EN.553.720. Prerequisites: one year of calculus. Corequisites: multivariable calculus and linear algebra.

Students who have received credit for AS.110.106 and/or AS.110.107 taken prior to Fall 2020 should contact the course instructor to determine whether they can receive permission to register for this course.

Prerequisites: AS.110.107 (Calculus II For Biological and Social Science) or AS.110.109 (Calculus II For Physical Sciences & Engineering) or AS.110.113 (Honors Single Variable Calculus). AS.110.201 (Linear Algebra) or AS.110.202 (Calculus III) or AS.110.211 (Honors Multivariable Calculus) OR AS.110.212 (Honors Linear Algebra) must also be taken prior to EN.553.310 or concurrently.

This is an introduction to statistics aimed at students in the life sciences. The course will provide the necessary background in probability with treatment of independence, Bayes theorem, discrete and continuous random variables and their distributions. The statistical topics covered will include sampling and sampling distributions, confidence intervals and hypothesis testing for means, comparison of populations, analysis of variance, linear regression and correlation. Analysis of data will be done using Excel.

Prerequisite: AS.110.106 (Calculus I For Biology and Social Sciences) or AS.110.108 (Calculus I For Physical Sciences and Engineering) or AS.110.113 (Single Multivariable Calculus).

Statistics Sequence restriction: Students who have completed any of these courses may not register: EN.550.230 (Introduction to Biostatistics) OR AS.280.345 (Public Health Biostatistics) OR AS.200.314 (Advanced Statistical Methods) OR EN.550.310 (Probability & Statistics) OR EN.550.311 (Probability and Statistics for the Biological Sciences and Engineering) OR EN.550.420 (Introduction to Probability) OR EN.550.430 (Introduction to Statistics) OR EN.560.348 (Probability & Statistics in Civil Engineering).