PRINCIPLES OF ECONOMICS

Equivalent to ECON UN1105, the first course for the major in economics. How a market economy determines the relative prices of goods, factors of production, and the allocation of resources; the circumstances under which it does these things efficiently. Why such an economy has fluctuations and how they may be controlled.

• Department: Summer Session (SUMM)
• MW 10:20 a.m.-11:55 a.m.
• Instructor: Nikita Raheja
  Info
• 4 points

First-Year Chinese II

In this course students will continue to develop basic communicative competence in Chinese. More emphasis will be given to reading and writing Chinese characters than First Year Chinese (I). In addition to bringing real life tasks into classroom and preparing students to use Chinese language to function in an immersive environment, the course also aims to cultivate inter-cultural communication awareness among students.

• Department: Summer Session (SUMM)
• MTWRF 10 a.m.-12:10 p.m.
• Instructor: Shaoyan Qi
  CULPA: 25 Info
• 5 points

THE LIFE AQUATIC

Water covers the majority of the earth’s surface but what of the life in these waters? Rivers, wetlands, lakes, estuaries and oceans provide habitat for an extraordinary diversity of animals. This course explores the amazing array of aquatic animals that occupy both freshwater and marine ecosystems as well as the natural and human activities that impact their survival. No previous knowledge of science is assumed. Fulfills the science requirement for most Columbia and GS undergraduates.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• Instructor: Mercer R Brugler
  Info
• 3 points

ACCELERATED ELEMENTARY TRANSL & READING

ACCELERAT ELEM TRANSL REA

Prerequisites: no previous knowledge of German required, but some background is strongly recommended. This accelerated survey of German grammar, reading techniques, and dictionary skills is designed primarily for graduate students preparing for reading proficiency exams or wishing to do research in German-language literature. In addition to translation, the course focuses on strategies for extracting general and specific information from German texts (skimming and scanning) and judging their relevance for a specific research purpose. Reading texts take students' fields of study into consideration. Although this course does not satisfy any part of the foreign language requirement for degree candidates, successful completion of the translation on the final exam fulfills the German reading proficiency requirement in most graduate programs. Students are advised that this course is a full-time commitment. Students should expect to study 2 hours every day for every hour spent in the classroom and additional time on weekends. Students who would like to gain speaking and listening skills are advised to enroll in the Intensive Elementary German I and II, or another appropriate German course. The Department of Germanic Languages will assist in selecting the appropriate course.

• Department: Summer Session (SUMM)
• MTWR 10 a.m.-12:05 p.m.
• Instructor: Christopher T Hoffman
  Info
• Instructor: Simona C Vaidean
  CULPA: 5 Info
• 4 points

INTENSIVE ELEM GERMAN I & II

This intensive program provides one year of German in one six-week session. The course enables students to understand, speak, read, and write in German about a range of subjects (such as: family activities, studies, work and home life, as well as travel, economics, and current events) and helps them develop an understanding of German speaking cultures. Classes are conducted in German and supplemented with written homework and audiovisual materials. Assignments and activities are diversified to integrate undergraduate and graduate students’ academic and personal interests. The program draws on the German heritage of New York City (museums, Goethe Institut, restaurants, etc.). Students are encouraged to attend German-language films and musical performances. Students have many opportunities for informal conversation. Upon successful completion of the course (with a minimum grade of B), students should achieve novice high to intermediate low proficiency (ACTFL scale). Final grades are based on frequent oral and written tests, writing assignments, a project on German culture in New York, and a final examination (written and oral). Students are advised that this course constitutes a full-time commitment. The workload of this course is very intense and students will be expected to spend 4-6 hours studying every day outside of class and additional time on weekends. The Department of Germanic Languages will assist in selecting the appropriate course. Equivalent to the combination of 
GERM UN1101
 and 
UN1102
 taught during the regular semesters.

If prior knowledge of German, a placement exam is required. Students should contact Jutta Schmiers-Heller (js2331) to schedule a test or if they have other questions about the course.

• Department: Summer Session (SUMM)
• MTWR noon-1:30 p.m.
• Instructor: Jutta Schmiers-Heller
  CULPA: 19 Info
• 6 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• MW 1 p.m.-4 p.m.
• MW 9 a.m.-12:10 p.m.
• Instructor: Holger A Klein
  CULPA: 13 Info
• Instructor: Alessandra Di Croce
  Info
• Instructor: John M Beeson
  Info
• Instructor: Alex Marko
  Info
• Instructor: Marina Correia
  Info
• Instructor: Janina P Marshall
  Info
• Instructor: Valerie J Zinner
  Info
• Instructor: Denise M Budd
  CULPA: 10 Info
• 3 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• MW 9 a.m.-12:10 p.m.
• MW 1 p.m.-4:10 p.m.
• 3 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• MW 1 p.m.-4:10 p.m.
• MW 5:30 p.m.-8:40 p.m.
• TR 9 a.m.-12:10 p.m.
• 3 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• TR 9 a.m.-12:10 p.m.
• TR 1 p.m.-4:10 p.m.
• 3 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• 3 points

Art Humanities

Discussion and analysis of the artistic qualities and significance of selected works of painting, sculpture, and architecture from the Parthenon in Athens to works of the 20th century.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• TR 5:30 p.m.-8:40 p.m.
• 3 points

ART HUMANITIES

ART HUMANITIES-PARIS

HUMA1121OC. Art Humanities (Paris). 3 points.

Art Humanities teaches students how to look at, think about, and engage in critical discussion of the visual arts. The course focuses on the formal structure of works of architecture, painting, and other media, as well as the historical context in which these works were made and understood. In addition to discussion-based classes like those held in New York, Art Humanities in Paris and in Berlin will make extensive use of the city through field trips to museums, buildings, and monuments. 
Please note that attendance at all class meetings, concerts, and excursions, unless otherwise indicated, is mandatory.

To enroll in this course in Paris
, you can apply to the
Columbia Summer Core In Paris: Art Humanities and Music Humanities
 through Undergraduate Global Engagement (UGE). Participants are required to take Music Humanities (HUMA1123OC) for 3 points alongside Art Humanities.  If you apply to the 
Columbia Summer in Paris: English Track
, you must take this course plus an additional 3-point course within the program.
 
Global Learning Scholarships
available. Tuition charges apply.

Please note the program dates are different from the Summer Sessions Terms. Visit the
UGE
website for the start and end dates for these programs. Email
uge@columbia.edu
with any questions you may have.

• Department: Global Programs
• Instructor: Ioannis Mylonopoulos
  CULPA: 13 Info
• Instructor: Irina T Oryshkevich
  CULPA: 11 Info
• Instructor: Barry G Bergdoll
  CULPA: 1 Info
• 3 points

Intensive Elem Italian:Venice

Italian In Venice, ITAL1121. Intensive Elementary Italian. 6 points

Instructor: TBD

Syllabus - Intensive Elementary

The equivalent of Italian 1101/1102 at Columbia. This intensive first year course, open to students with no previous training in Italian, prepares students to move into intermediate Italian.

The course provides students with a foundation in the four language skills of listening, speaking, reading and writing. Students are encouraged to participate actively in class discussions and activities and to interact with teacher and classmates. We will learn Italian not only thanks to exercises and conversation, but also through songs, clips, pictures, food, and games. Upon successful completion of the course, students should be able to:


provide basic information in Italian about themselves, their interests, their daily activities;

participate in a conversation on everyday topics using the major time frames of present and past;read short edited texts, understand the main ideas, and pick out important information from authentic texts (e.g. menus, signs, train schedules, etc.)

write short compositions on familiar topics;

identify basic cultural rituals and practices in the context of their occurrence.


Please note:  If you have completed Elementary 1, you are welcome to enroll in the Intensive Elementary course. You will be expected to enroll in the full 6 point course. While there will be some overlap in the coursework that you already completed at Columbia, it will benefit you to be in Venice to reinforce and enhance your language studies before continuing on to new material. Upon successful completion of the course, you will be awarded 4 points for the Intensive course.

To enroll in this course, you must apply to the
 
Columbia in Venice
 
program through the Center for Undergraduate Global Engagement (UGE).
 
Global Learning Scholarships 
available. 
Tuition
 charges apply.

• Department: Global Programs
• Instructor: Ricardo A Belisario
  Info
• 6 points

INTENSIVE ELEMENTARY LATIN

Equivalent to Latin 1101 and 1102. Covers all of Latin grammar and syntax in one term to prepare the student to enter Latin 1201 or 1202. This is an intensive course with substantial preparation time outside of class.

• Department: Summer Session (SUMM)
• MTWR 9 a.m.-12:10 p.m.
• Instructor: Kristina Milnor
  CULPA: 21 Wikipedia h-index: 10 Info
• 6 points

MUSIC HUMANITIES

MUSIC HUMANITIES: PARIS

HUMA1123OC. Music Humanities (Paris). 3 points.

The focus of Music Humanities is the masterpieces of Western art music in their historical and cultural contexts. The specific goals of the course are to awaken and encourage an appreciation of Western music, to help the student learn to respond intelligently to a variety of musical idioms, and to engage the student in the issues of various debates about the character and purposes of music that have occupied composers and musical thinkers since ancient times. Students become actively involved in the process of critical listening both in the classroom and in the live performances that are as central to the course in Berlin and in Paris as in New York. Using a “great works” approach, the course will look at the changing genres and styles of music, examining composers’ choices and assumptions, as well as those of their patrons and audiences, as it moves chronologically from the Middle Ages to the present. 
Please note that attendance at all class meetings, concerts, and excursions, unless otherwise indicated, is mandatory.

To enroll in this course in Paris
, you can apply to the 
Columbia Summer Core In Paris: Art Humanities and Music Humanities
 through Undergraduate Global Engagement (UGE). Participants are required to take Art Humanities (HUMA1121OC) for 3 points alongside Music Humanities.  If you apply to the 
Columbia Summer in Paris: English Track
, you must take this course plus an additional 3-point course within the program.
 
Global Learning Scholarships 
available. Tuition charges apply.

Please note the program dates are different from the Summer Sessions Terms. Visit the 
UGE
 website for the start and end dates for these programs. Email 
uge@columbia.edu
 with any questions you may have.

Please email 
uge@columbia.edu
 with any questions you may have.

• Department: Global Programs
• Instructor: Walter M Frisch
  CULPA: 17 Info
• Instructor: Mariusz Kozak
  CULPA: 4 h-index: 5 Info
• Instructor: Magdalena Baczewska
  CULPA: 4 Info
• 3 points

Music Humanities

Analysis and discussion of representative works from the Middle Ages to the present.

• Department: Summer Session (SUMM)
• TR 9 a.m.-12:10 p.m.
• MW 1 p.m.-4:10 p.m.
• MW 5:30 p.m.-8:40 p.m.
• TR 9 a.m.-12:10 p.m.
• Instructor: Peter M Susser
  CULPA: 20 Info
• 3 points

Music Humanities

Analysis and discussion of representative works from the Middle Ages to the present.

• Department: Summer Session (SUMM)
• TR 9 a.m.-12:10 p.m.
• TR 1 p.m.-4:10 p.m.
• TR 5:30 p.m.-8:40 p.m.
• MW 9 a.m.-12:10 p.m.
• MW 1 p.m.-4:10 p.m.
• MW 5:30 p.m.-8:40 p.m.
• MW 9 a.m.-12:10 p.m.
• TR 1 p.m.-4:10 p.m.
• 3 points

Music Humanities

Analysis and discussion of representative works from the Middle Ages to the present.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• TR 5:30 p.m.-8:40 p.m.
• Instructor: Knar Abrahamyan
  Info
• 3 points

PRINCIPLES OF ECONOMICS-DISC

Required Discussion section for ECON UN1105 Principles of Economics

• Department: Summer Session (SUMM)
• 0 points

INTERMEDIATE FRENCH I

• Department: Summer Session (SUMM)
• MTWR 10 a.m.-12:05 p.m.
• Instructor: Sophie Queuniet
  CULPA: 7 Info
• Instructor: Hayet Sellami
  CULPA: 3 Info
• 4 points

INTERMEDIATE ITALIAN I

Prerequisites: ITAL V1102 or W1102, or the equivalent. If you did not take Elementary Italian at Columbia in the semester preceding the current one, you must take the placement test, offered by the Italian Department at the beginning of each semester. Same course as ITAL V1201-V1202.

• Department: Summer Session (SUMM)
• MTWR 11:30 a.m.-1:35 p.m.
• Instructor: Alessandra Saggin
  CULPA: 4 Info
• 4 points

CALCULUS III

Prerequisites: MATH S1102, or the equivalent. Columbia College students who aim at an economics major AND have at least the grade of B in Calculus I may take Calculus III directly after Calculus I. However, all students majoring in engineering, science, or mathematics should follow Calculus I with Calculus II. Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• TR 9 a.m.-12:10 p.m.
• 3 points

GENERAL PHYSICS I

Prerequisites: this course uses elementary concepts from calculus, and students should therefore have some basic background in differentiation and integration. Assignments to discussion sections are made after the first lecture. Basic introduction to the study of mechanics, fluids, and thermodynamics. The accompanying laboratory is PHYS S1291D. NOTE: There are two recitation sessions that meet for one hour each week. The recitation times will be selected at the first class meeting.

• Department: Summer Session (SUMM)
• MTWR 9 a.m.-10:25 a.m.
• Instructor: Eric Raymer
  CULPA: 3 Info
• 3 points

CALC-BASED INTRO TO STATISTICS

Prerequisites: working knowledge of calculus (differentiation and integration). Designed for students who desire a strong grounding in statistical concepts with a greater degree of mathematical rigor than in STAT W1111. Random variables, probability distributions, pdf, cdf, mean, variance, correlation, conditional distribution, conditional mean and conditional variance, law of iterated expectations, normal, chi-square, F and t distributions, law of large numbers, central limit theorem, parameter estimation, unbiasedness, consistency, efficiency, hypothesis testing, p-value,confidence intervals. maximum likelihood estimation. Satisfies the pre-requisites for ECON W3412.

• Department: Summer Session (SUMM)
• MTWR 10:45 a.m.-12:20 p.m.
• MTWR 6:15 p.m.-7:50 p.m.
• 3 points

POETRY WRITING WORKSHOP

The Poetry Writing Workshop is designed for all students with a serious interest in poetry writing, from those who lack significant workshop experience or training in the craft of poetry to seasoned workshop participants looking for new challenges and perspectives on their work. Students will be assigned writing exercises emphasizing such aspects of verse composition as the poetic line, the image, rhyme and other sound devices, verse forms, repetition, collage, and others. Students will also read an variety of exemplary work in verse, submit brief critical analyses of poems, and critique each others original work.

• Department: Summer Session (SUMM)
• TR 5:30 p.m.-8:40 p.m.
• Instructor: Timothy B Donnelly
  Info
• Instructor: Dorothea S Lasky
  Wikipedia Info
• 3 points

INTERMEDIATE FRENCH II

• Department: Summer Session (SUMM)
• MTWR 10 a.m.-12:05 p.m.
• Instructor: Alexandra Borer
  CULPA: 4 Info
• Instructor: Marie-Helene Koffi-Tessio
  CULPA: 1 Info
• 4 points

INTERMEDIATE ITALIAN II

Prerequisites: ITAL V1201 or W1201, or the equivalent. If you did not take Elementary Italian at Columbia in the semester preceding the current one, you must take the placement test, offered by the Italian Department at the beginning of each semester. A review of grammar, intensive reading, composition, and practice in conversation. Exploration of literary and cultural material. Lab: hours to be arranged. ITAL V1202 fulfils the basic foreign language requirement and prepares students for advanced study in Italian language and literature.

• Department: Summer Session (SUMM)
• MTWR 4:30 p.m.-6:35 p.m.
• Instructor: Patrizia Palumbo
  CULPA: 15 Info
• 4 points

GENERAL PHYSICS II

Prerequisites: PHYS S1201 or the equivalent. This course uses elementary concepts from calculus, and students should therefore have some basic background in differentiation and integration. The same course as PHYS S1202X, but given in a six-week session. Assignments to discussion sections are made after the first lecture. Basic introduction to the study of electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics. The accompanying laboratory is PHYS S1292Q. NOTE: There are two recitation sessions that meet for one hour each week. The recitation times will be selected at the first class meeting.

• Department: Summer Session (SUMM)
• MW 6 p.m.-7:25 p.m.
• MTWR 9 a.m.-10:25 a.m.
• Instructor: Nicholas M Luber
  Info
• Instructor: Rebecca I Grossman
  CULPA: 3 Info
• 3 points

Intensive Inter Italian:Venice

Italian in Venice ITAL1203OC. Intensive Intermediate Italian. 6 points.  
Prerequisites: One year of college-level Italian or the equivalent. 

Instructor: Luca Abbattista

The equivalent of Italian 1201/1202. This intensive second year course allows students to develop listening, speaking, reading, and writing skills in Italian and a better understanding of Italian culture. Students are involved in activities outside the classroom, where they gather information on Italian cultural topics through interviews and surveys that allow them to engage directly with the local community. Upon successful completion of this course, students should be able to:



use a sufficient range of language to be able to give clear description;



express viewpoints on most general topics;



show a relatively high degree of grammatical control;



use cohesive devices to link their utterances into clear and coherent discourse;



give detailed descriptions and presentations on a wide range of subjects related to their fields of interest, expanding and supporting their ideas;



write clear and detailed text on a variety of subjects related to their field of interest, synthesizing and evaluating information and arguments;



understand straightforward factual information about common everyday life;



interact with a degree of fluency and spontaneity that makes for regular interaction;



express news and views effectively in writing, and relate to those of others;



express themselves appropriately in different cultural and communicative situations;



and be aware of the most significant differences between the customs, usages, attitudes, values, and beliefs prevalent in the Italian culture and those of their own.



Please note: If you have completed Intensive 1, you are welcome to enroll in the Intensive Intermediate course. You will be expected to enroll in the full 6-point course. While there will be some overlap in the coursework that you already completed at Columbia, it will benefit you to be in Venice to reinforce and enhance your language studies before continuing on to new material. Upon successful completion of the course, you will be awarded 4 points for the Intensive course.

To enroll in this course, you must apply to the
&

• Department: Global Programs
• Instructor: Matteo Heilbrun
  Info
• 6 points

Accel Intermed French: Paris

Accelerated Intermediate French FREN1205OC.  6 points.

Instructor: 
 
Karen Santos Da Silva
, Senior Lecturer of French at Barnard College

On this program, students will prepare for advanced French language and culture with an emphasis on developing highly accurate speaking, reading, and writing skills. While we will read a variety of French and Francophone primary texts, the most important primary text with which students will be engaging on a daily basis is Paris and its diverse inhabitants.

At the conclusion of this course, students will


be able to communicate with French native speakers and navigate living in Paris with ease

be able to confidently express simple concepts in written and spoken French, and begin to express abstract ideas in written and spoken French

be able to describe, narrate, and analyze their cultural experiences orally

have a better mastery of French pronunciation, and colloquial French

have a solid base of knowledge about French and Francophone culture


To enroll in this course, you must apply to the
 
Columbia Summer Accelerated French in Paris
 
program through the Center for Undergraduate Global Engagement (UGE).
 
Global Learning Scholarships 
available.
Tuition
 
charges apply. 

Please note the program dates are different from the Summer Sessions Terms. Visit the

UGE
website for the start and end dates for the Columbia Summer Accelerated French in Paris program.

Please email
uge@columbia.edu

with any questions you may have.

• Department: Global Programs
• 6 points

FIRST YEAR ARABIC I

Prerequisites: Students that are not registering for MDES S1211 will be required to request professor permission (tb46@columbia.edu) to enroll.

• Department: Summer Session (SUMM)
• MTWRF 9 a.m.-1 p.m.
• Instructor: May Ahmar
  CULPA: 9 Info
• 5 points

FIRST YEAR ARABIC II

Prerequisites: MDES S1210, or the equivalent.

• Department: Summer Session (SUMM)
• MTWRF 9 a.m.-1 p.m.
• Instructor: Reem Faraj
  CULPA: 4 Info
• 5 points

Foundations of Science

Using modern, student-centered, active and collaborative learning techniques, students will engage — through field observations, in-class experiments, computer simulations, and selected readings — with a range of ideas and techniques designed to integrate and anchor scientific habits of mind. Throughout the term, all students will satisfy a detailed set of rubrics by documenting their learning in reflection postings designed to serve as a future reference for how they, individually, went from not understanding an idea to understanding it. Topics covered will include statistics, basic probability, a variety of calculational skills, graph reading, and estimation — all aimed at elucidating such concepts as energy, matter, cells, and genes in the context of astronomy, biology, chemistry, earth science, neuroscience, and physics.

• Department: Summer Session (SUMM)
• W 1 p.m.-5 p.m.
• Instructor: Klejda Bega
  Info
• 4 points

SECOND YEAR ARABIC I

Prerequisites: MDES UN1211-UN1212, or the equivalent.

• Department: Summer Session (SUMM)
• MTWRF 9 a.m.-1 p.m.
• Instructor: Nasr Abdo
  Info
• 5 points

SECOND YEAR ARABIC II

Prerequisites: Prerequisites: MDES UN1211-UN1212 and UN1214 or the equivalent.

• Department: Summer Session (SUMM)
• MTWRF 9 a.m.-1 p.m.
• Instructor: Ouijdane Absi
  CULPA: 6 Info
• 5 points

INTENSIVE INTERMEDIATE LATIN

• Department: Summer Session (SUMM)
• MTWR 9 a.m.-12:10 p.m.
• Instructor: Umberto Verdura
  Info
• 6 points

GENERAL PHYSICS LAB I

Prerequisites: PHYS S1201. May be taken before or concurrently with this course. Laboratory for PHYS S1201D. Assignments to laboratory sections are made after the first lecture, offered Mon/Wed or Tues/Thurs 10.30AM-1.30PM.

• Department: Summer Session (SUMM)
• MTWR 11:30 a.m.-2:30 p.m.
• Instructor: Giuseppina C Cambareri
  Info
• 1 points

GENERAL PHYSICS LAB I

Prerequisites: PHYS S1201. May be taken before or concurrently with this course. Laboratory for PHYS S1201D. Assignments to laboratory sections are made after the first lecture, offered Mon/Wed or Tues/Thurs 10.30AM-1.30PM.

• Department: Summer Session (SUMM)
• MTWR 11:30 a.m.-2:30 p.m.
• Instructor: Giuseppina C Cambareri
  Info
• 1 points

GENERAL PHYSICS LAB II

Prerequisites: PHYS S1202. May be taken before or concurrently with this course. Laboratory for PHYS 1202X. Assignments to laboratory sections are made after the first lecture. NOTE: Labs meet one day a week (Mon, Tues, Wed or Thurs) 1:00pm - 4:00pm only. There are no evening lab sections.

• Department: Summer Session (SUMM)
• M 1 p.m.-4 p.m.
• T 1 p.m.-4 p.m.
• W 1 p.m.-4 p.m.
• R 1 p.m.-4 p.m.
• MTWR 11:30 a.m.-2:30 p.m.
• Instructor: Giuseppina C Cambareri
  Info
• 1 points

GENERAL PHYSICS LAB II

Prerequisites: PHYS S1202. May be taken before or concurrently with this course. Laboratory for PHYS 1202X. Assignments to laboratory sections are made after the first lecture. NOTE: Labs meet one day a week (Mon, Tues, Wed or Thurs) 1:00pm - 4:00pm only. There are no evening lab sections.

• Department: Summer Session (SUMM)
• MTWR 11:30 a.m.-2:30 p.m.
• Instructor: Giuseppina C Cambareri
  Info
• 1 points

Calculus I

Calculus I
Material includes the study of limits, derivatives, and applications of derivatives, as well as an introduction to integrals. Success in this course requires intense commitment to study and collaboration both in and out of class, along with active participation during class, and the ability to follow both written and verbal directions.   
The overarching objective of the course is for students to develop conceptual fluency and computational competence working with limits, derivatives, and their applications.   Students will enhance their quantitative reasoning, particularly through interpreting/analyzing charts and graphs in the study of limits and derivatives.  Problem solving skills will be augmented through applied word problems, particularly relating to optimization, related rates, and graphing.  Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. While collaborative projects will advance their ability to do so orally and visually.

• Department: BARNARD SUMMER PROGRAMS
• MTWR 4:30 p.m.-6:05 p.m.
• Instructor: Lindsay C Piechnik
  CULPA: 15 Info
• 3 points

Calculus III

Prerequisite for Calc III is Calc I.  
For exam placement, see dept site: https://math.barnard.edu/placement-calculus-classes


To develop a conceptual understanding of the fundamental principles of multivariable differential calculus and explore their practical relevance to other branches of natural and social sciences.

Students will enhance their critical thinking by using 3D graphical tools and engaging with three dimensional representations of curves, surfaces and solids.

Writing justifications/explanations for answers on all graded work will expand students' ability to clearly communicate mathematical ideas in writing. 

Problem solving skills will be augmented through applications in physics and real world problems involving the dynamics of movement, and optimization problems involving multiple inputs (parameters)




The sequence of topics covered is as follows.



​​​​1.  
Vectors. Equations of lines and planes. Cylinders and quadric surfaces.
 



2. Vector functions. Space curves. Arc length and curvature. Applications.



3. 
Functions of several variables. Partial derivatives. Gradient. Optimization. Lagrange multipliers.

• Department: BARNARD SUMMER PROGRAMS
• TR 1 p.m.-4:10 p.m.
• Instructor: Chris Ivanov
  Info
• 3 points

COLLOQUIUM ON MAJOR TEXTS

Readings in translation and discussion of texts of Middle Eastern and Indian origin. Readings may include the Quran, Islamic philosophy, Sufi poetry, the Upanishads, Buddhist sutras, the Bhagavad Gita, Indian epics and drama, and Gandhis Autobiography.

• Department: Summer Session (SUMM)
• MR 1 p.m.-5 p.m.
• Instructor: Elaine Van Dalen
  CULPA: 3 Info
• 4 points

EARTH, MOON AND PLANETS

Prerequisites: Recommended preparation: a working knowledge of high school algebra. May be counted toward the science requirement for most Columbia University undergraduate students. The overall architecture of the solar system. Motions of the celestial sphere. Time and the calendar. Major planets, the earth-moon system, minor planets, comets. Life in the solar system and beyond.

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• Instructor: James H Applegate
  CULPA: 44 Info
• 3 points

GENERAL CHEMISTRY I-LECTURES

Prerequisites: high school chemistry and algebra, CHEM S0001, or the department's permission. Topics include stoichiometry, states of matter, nuclear properties, electronic structures of atoms, periodic properties, chemical bonding, molecular geometry, introduction to quantum mechanics and atomic theory, introduction to organic, biological chemistry and inorganic coordination chemistry. Topical subjects may include spectroscopy, solid state and materials science, polymer science and macromolecular structures. The order of presentation of topics may differ from the order presented here. Students are required to attend the separate daily morning recitations which accompany the lectures (total time block: MTWR 9:30-12:20). Registering for CHEM S1403D will automatically register students for the recitation section. Students who wish to take the full sequence of General Chemistry Lectures and General Chemistry Laboratory should also register for CHEM S1404Q and CHEM S1500 (see below). This course is equivalent to CHEM W1403 General Chemistry I Lecture.

• Department: Summer Session (SUMM)
• MTWR 9:30 a.m.-12:20 p.m.
• Instructor: Jason G Polisar
  CULPA: 4 Info
• 4 points

STARS, GALAXIES & COSMOLOGY

ASTR UN1404: In this course, we will explore how stars, galaxies, and the Universe formed and changed over time. We will have a combination of lectures, class discussions, and hands-ons activities to examine concepts including: distances to, and fundamental properties of, nearby stars; nucleosynthesis and stellar evolution; novae and supernovae; galaxies; the structure of the universe and theories concerning its origin, evolution, and
ultimate fate. This course will use algebra, but ample math support will be provided. You can only receive credit for ASTR UN1404 if you have not taken ASTR BC1754, ASTR UN1420 or ASTR UN1836

• Department: Summer Session (SUMM)
• TR 1 p.m.-4:10 p.m.
• Instructor: Amanda C Quirk
  Info
• 3 points

GENERAL CHEMISTRY II-LECTURES

Prerequisites: CHEM S1403 General Chemistry I Lecture or the equivalent. Topics include gases, kinetic theory of gases, states of matter: liquids and solids, chemical equilibria, acids and bases, applications of equilibria, thermochemistry and spontaneous processes (energy, enthalpy, entropy, free energy) as well as chemical kinetics and electrochemistry. The order of presentation of topics may differ from the order presented here. Students must also attend the daily morning recitations which accompany the lectures (total time block: MTWR 9:30-12:20). Registering for CHEM S1404Q will automatically register students for the recitation section. The continuation of CHEM S1403D General Chemistry I Lecture. Students who wish to take the full sequence of General Chemistry Lectures and General Chemistry Laboratory should also register for CHEM S1403D and CHEM S1500 (see below). This course is equivalent to CHEM UN1404 General Chemistry II Lecture.

• Department: Summer Session (SUMM)
• MTWR 9:30 a.m.-12:20 p.m.
• TR 6:10 p.m.-7:35 p.m.
• Instructor: Jason G Polisar
  CULPA: 4 Info
• Instructor: Ruben M Savizky
  CULPA: 22 Info
• 4 points

GENERAL CHEMISTRY II-REC

Corequisites: CHEM S1404X. To be enrolled in CHEM S1404X, you must be enrolled in CHEM S1406X.

• Department: Summer Session (SUMM)
• T 5 p.m.-5:50 p.m.
• T 8 p.m.-8:50 p.m.
• R 5 p.m.-5:50 p.m.
• Instructor: Ruben M Savizky
  CULPA: 22 Info
• 0 points

EXPERIMNTL PSYCH:HUMN BEHAVIOR

Introduction to the techniques of research employed in the study of human behavior. Students gain experience in the conduct of research, including design of simple experiments, observation and measurement techniques, and the analysis of behavioral data.

• Department: Summer Session (SUMM)
• MTWR 10:45 a.m.-12:50 p.m.
• Instructor: Patricia G Lindemann
  CULPA: 64 Info
• 4 points