Columbia Combined Plan Course Mapping

Yeshiva University – Columbia Combined Plan Course Mapping

Ed Berliner [email protected] Room 1311 Belfer Hall Yeshiva University 500 W. 185 St. New York, NY 10033

2016-2017 PRE-COMBINED PLAN CURRICULUM MAPPING GUIDE

This document has been written to correlate the Columbia University Combined Plan requirements for each Engineering Major with available Y.U. course offerings. Section A are the foundation courses required for all Majors; Section B are the Major specific course requirements. Generally, the Columbia requirements are presented in normal text, and the YU courses follow the phrase “Met By” and are presented in bold text. If the term “Both Courses” is used, Both must must taken to satisfy the requirement. Appendices I, II, and III are the descriptions of referred to courses at Stern College for Women (SCW), Yeshiva College, (YC), and SYMS School of Business respectively.

In order to be considered for guaranteed admission, students must successfully complete the Y.U. equivalents of the below listed Columbia courses. If you have any questions, please consult with Dr. Ed Berliner (YC), Dr. Anatoly Frenkel/Dr. Ed Berliner (SCW), or any of the College advisors. Please also contact Dr. Berliner If you have a question about a specific requirement or about other ways to fulfill prerequisites if Y.U. does not offer a required course required by Columbia.

Students who are participating in the BA/BS Combined Plan can either Major in Pre- Engineering (YC), Pre-Engineering or Physical Science (SCW), or any valid major provided that all Columbia Foundation and Major specific requirements have been met. Columbia requires (no exceptions) that all applicants for the BA/BS Combined Plan have an overall 3.3 GPA, and a 3.3 GPA (calculations based on the first time a course is taken) with no grade lower than B in all the required courses presented below. In addition, all YU requirements for graduation must be met with the exception of the total number of credits.

This document is a guide; always consult the Official Columbia Requirements Document as that could change on short notice and could be out of synch with this guide.

For more information, please visit the website at http://www.yu.edu/yeshiva-college/ug/pre-engineering/ or http://www.yu.edu/stern/ug/physics/ or e-mail [email protected].

A. FOUNDATION COURSES REQUIRED OF ALL MAJORS:

i. MATHEMATICS - Columbia requires the equivalent of their full sequence of Calculus I, II, III (UN1101, UN1102, UN1201). This is fulfilled by the Y.U. 3 semester Calculus sequence.

Met by a. SCW -- MATH 1412, MATH 1413 Calculus I, II (4 credits each) YC -- MAT 1412, MATH 1413 Calculus I, II (4 credits each)

b. SCW - MATH 1510 Multivariable Calculus 3(4 credits) YC - MAT 1510 Multivariable Calculus 3(4 credits) ii. PHYSICS - Columbia requires the equivalent of the first 2 semesters of Calculus based First Year Physics: Mechanics and Thermodynamics (UN1401), and Electricity, Magnetism, and Optics (UN1402). This is fulfilled by the Y.U. 2 semester sequence.

Met by a. SCW - PHYS 1041C, 1042C General Physics – Lectures & Lab (5 credits)

b. YC (Both Courses) i. PHY1051R, 1052R General Physics—Lectures (4 credits) ii. PHY 1061L, 2061L General Physics— Laboratory (1 credit) iii. CHEMISTRY – Columbia requires the equivalent of General Chemistry I (UN1403). They also note that some programs require an additional second semester of General Chemistry (C1404) or have possible substitutions. Columbia 1403/1404 is fulfilled by the Y.U. 2 Semester Sequence.

Met by i. SCW - CHEM 1045C General Chemistry – Lectures & Lab (4 credits)

ii. YC - CHE 1045R General Chemistry I (Lecture) (3 credits) iv. LAB REQUIREMENT- Columbia requires that either a one-semester Physics lab or one-semester Chemistry lab is generally required, depending on the individual field of study chosen. Because SCW bundles the Lab with the Lecture, this requirement is automatically fulfilled. Because Y.C. states that Physics Labs are co-requisites, this requirement is automatically fulfilled. When a first year Chem Lab is required for a Y.C. student, will be fulfilled by CHE 1047L General Chemistry I (Lab) (2 credits) v. COMPUTER SCIENCE - Columbia requires the Introduction to computer science and programming in C++, JAVA , Python, or MATLAB (W1003, W1004, W1005, W1007 or ENGI E1009). This is fulfilled by the following Y.U. course.

Met by i. SCW - COMP 1300C Introduction to Computer Science and Programming (4 credits). This course uses PYTHON

ii. YC - COM 1300C Introduction to Computer Science and Programming (4 credits) This course uses JAVA vi. HUMANITIES AND SOCIAL SCIENCES – Columbia requires Twenty-seven-(27) non-technical credit hours. These courses must include the equivalent of the following 2 Columbia courses: Principles of Economics (ECON UN1105) and English Composition (ENGL CC1010 University Writing).The last 2 are fulfilled by the following Y.U. courses.

Met by a. SCW (Both Courses) i. ECON 1010 Principles of Economics (3 credits)

ii. One of the two listed below 1. ENGL 1100 Composition and Rhetoric (3 credits) 2. ENGL 1200H Freshman Honors Seminar (3 credits) b. YC (Both Courses) i. ECON 1010 Principles of Economics (3 credits) ii. ENG 1020 First Year Writing (3 credits)

B. REQUIRED COLUMBIA ENGINEERING MAJOR SPECIFIC COURSES (Notes in italics clarify requirements.)

APPLIED MATHEMATICS or APPLIED PHYSICS

MATHEMATICS – Columbia Required  Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Courses

 Ordinary Differential Equations (UN1210)

Met By  SCW -- MATH 2601 Differential Equations (3 credits)  YC -- MAT 2601 Differential Equations (3 credits)

PHYSICS – Columbia Required  Classical and Quantum Waves (UN1403)

Met By  SCW – Both Courses Listed Below o PHYS 2051 Waves and Optics (3 credits) o PHYS 2052 Modern Physics (3 credits)

 YC – Both Courses Listed Below o PHY 2051 Waves and Optics (3 credits) o PHY 2052 Introduction to Modern Physics (3 credits)

 Physics Lab (UN1493/4) Met By  SCW – PHYS 1041C/1042C General Physics  YC – PHY 1061L/2061L General Physics

CHEMISTRY / BIOLOGY – Columbia required -- (choose one course listed below. Chemistry/Biology labs not required.)  General Chemistry I (UN1403)

Met By  SCW – CHEM 1045C General Chemistry (4 Credits)  YC –CHE 1045R General Chemistry(3 Credits)

 Environmental Biology: Molecules to Cells (EEEB UN2001)

Met By  SCW - BIOL 3038C Ecology (4 credits)  YC - BIO 3038C Ecology (4 credits)

 Introduction to Molecular and Cellular Biology (UN2005)

Met By  SCW - Both Courses o BIOL 3207C Cell Biology (4 credits) o BIOL 3521C Molecular Biology (4 credits)

 YC - Both Courses o BIO 3207C Cell Biology (4 credits) o BIO 3521C Molecular Biology (4 credits)

BIOMEDICAL ENGINEERING (ALL TRACKS)

MATHEMATICS  Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Introduction to applied mathematics Ordinary Differential Equations & Linear Algebra (APMA E2101). Students who take an ODE course must also take a Linear Algebra course. Met By  SCW– Both Courses o MATH 2601 Differential Equations (3 credits) o MATH 2105 Linear Algebra (3 credits)

 YC– Both Courses o MAT 2601 Differential Equations (3 credits) o MAT 2105 Linear Algebra (3 credits).

PHYSICS  Classical and Quantum Waves (UN1403)

Met By  SCW – Both Courses Listed Below o PHYS 2051 Waves and Optics (3 credits) o PHYS 2052 Modern Physics (3 credits)  YC – Both Courses o PHY 2051 Waves and Optics (3 credits) o PHY 2052 Introduction to Modern Physics (3 credits)

CHEMISTRY  General Chemistry II (UN1404)

Met By  SCW– CHEM 1046 General Chemistry (4 Credits)  YC – CHE 1046 General Chemistry (3 Credits)

 General Chemistry Lab (UN1500)

Met By  SCW– CHEM 1045C  YC – CHE 1047L

BIOLOGY  Introduction to Biology I and II (BIOL UN2005 and UN2006) Met By  SCW– BIOL 1011C, BIOL 1012C (4 Credits)  YC – BIO 1011R, BIO 1012R (3 Credits)

ELECTRICAL ENGINEERING  Introduction to Electrical Engineering (ELEN E1201) [may be taken the summer before entering or while at Columbia] There is no current SCW/YC Course that meets this requirement.

COMPUTER SCIENCE  Python Language (ENGI E1006) Required

Met By  SCW– COMP 1300 Introduction to Computer Science and Programming JAVA (4 credits)  YC – COM 1504 Discrete Structures (PYTHON) (4 credits)

CHEMICAL ENGINEERING

MATHEMATICS

 Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Ordinary Differential Equations (UN2030) or Introduction to applied mathematics -- Ordinary Differential Equations & Linear Algebra (APMA E2101)

Met By  SCW– Both Courses o MATH 2601 Differential Equations (3 credits) o MATH 2105 Linear Algebra (3 credits)

 YC– Both Courses o MAT 2601 Differential Equations (3 credits) o MAT 2105 Linear Algebra (3 credits)

PHYSICS  Physics Lab (UN1493/4)

Met By  SCW– Both Courses -- PHYS 1041C/1042C  YC – Both Courses -- PHY 1061L/2061L

CHEMISTRY  General Chemistry II (UN1404)  General Chemistry Lab (UN1500)  Organic Chemistry I (UN2443)  Organic Chemistry Lab (UN2943)

Met By  SCW – Both Courses o CHEM 1046C General Chemistry (4 Credits) o CHEM 1213C Organic Chemistry (5 Credits)  YC – Both Courses o CHE 1046R General Chemistry (3 Credits) o CHE 1047L General Chemistry Lab (2 Credits) o YC – CHE 1213 Organic Chemistry R&L (5 Credits) Computer Science (choose one course listed below)  Python Language (ENGI E1006) Required

Met By  SCW– COMP 1300 Introduction to Computer Science and Programming (PYTHON) (4 credits)  YC – COM 1504 Discrete Structures (PYTHON) (4 credits)

CIVIL ENGINEERING

MATHEMATICS  Introduction to applied mathematics Ordinary Differential Equations & Linear Algebra (APMA E2101) Students who take an ODE course must also take a Linear Algebra course.

Met By  SCW– Both Courses o MATH 2601 Differential Equations (3 Credits) o MATH 2105 Linear Algebra (3 Credits)  YC – Both Courses o MAT 2601 Differential Equations (3 credits) o MAT 2105 Linear Algebra (3 Credits)

GEOLOGY (choose one course listed below)  Earth: Origin, Evolution, Processes Future (EESC V1011)

Met By  There are no Geology Courses in YC/SCW. Civil Engineering students should meet with the Pre-Engineering Advisor to obtain direction from Columbia as to how and when these courses should be taken.

ENGINEERING MECHANICS  Mechanics (ENME E3105) [may be taken the summer before entering or while at Columbia]

Met By

 SCW – Both Courses must be taken to cover Rigid Bodies o PHYS 1221 Classical Mechanics I (3 Credits) o PHYS 1222 Classical Mechanics II (3 Credits)  YC – Both Courses must be taken to cover Rigid Bodies o PHY 1221 or 1221H Classical Mechanics (3 Credits) o PHY 1222 Advanced Mechanics (3 Credits)

COMPUTER SCIENCE  Introduction to Computer Science and Programming in MATLAB (COMS W1005) preferred

Met By  SCW– COMP 1300 Introduction to Computer Science and Programming (4 credits). Columbia may require a MATLAB course once there.  YC – COM 1300 Introduction to Computer Science and Programming (4 credits) Columbia may require a MATLAB course once there.

COMPUTER ENGINEERING

MATHEMATICS

 Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Introduction to applied mathematics Ordinary Differential Equations & Linear Algebra (APMA E2101). Students who take an ODE course must also take a Linear Algebra course.

COMPUTER SCIENCE (Computer Programming in JAVA is required.)  Discrete Mathematics (COMS W3203). Knowledge of JAVA is required (W1004). YC students get this is their Introductory Course. SCW students have to take the additional course.

Met By  SCW – Both Courses o COMP 3650 Object Oriented Programming ---JAVA – (3 credits) o COMP 1504 Discrete Structures (3 credits)  YC -- COM 1504 Discrete Structures (4 credits)

COMPUTER SCIENCE

COMPUTER SCIENCE (Computer Programming in JAVA is required)  JAVA Skills

Met By  SCW -- COMP 3650 Object Oriented Programming ---PYTHON – (3 credits)  YC -- Introduction to Computer Science and Programming (4 credits) This course uses JAVA

 Data Structures and Algorithms (COMS W3137)

Met By  SCW - COMP 1320C Introduction to Data Structures (4 credits)  YC - COM 1320 Data Structures (4 credits)

 Discrete Mathematics (COMS W3203)

Met By  SCW -- COMP 1504 Discrete Structures (3 credits)  YC -- COM 1300 Discrete Structures (4 credits)

EARTH AND ENVIRONMENTAL ENGINEERING

MATHEMATICS  Introduction to applied mathematics Ordinary Differential Equations & Linear Algebra (APMA E2101).Students who take an ODE course must also take a Linear Algebra course.

Met By  SCW– Both Courses  MATH 2601 Differential Equations (3 Credits)  MATH 2105 Linear Algebra (3 Credits)  YC – Both Courses  MAT 2601 Differential Equations (3 credits)  MAT 2105 Linear Algebra (3 Credits)

 Introduction to Probability and Statistics (W3600) (This may be taken during enrollment at Columbia.). This course must have calculus, including multivariable integration, as a pre-requisite.

Met By  SCW – Both Courses o MATH 2461 Probability Theory (3 credits) o MATH 2462 Mathematical Statistics (3 credits)

 YC – Both Courses

o MAT 2461 Probability Theory (3 credits) o MAT 2462 Mathematical Statistics (3 credits)

CHEMISTRY  General Chemistry II (UN1404)

Met By  SCW– CHEM 1046 General Chemistry (4 Credits)  YC – CHE 1046 General Chemistry (3 Credits)

 General Chemistry Lab (UN1500) Met By  SCW– CHEM 1045C  YC – CHE 1047L

OTHER SCIENCE ELECTIVE (choose one course listed below)  Organic Chemistry (CHEM UN2443)

Met By  SCW – CHEM 1213C Organic Chemistry (5 Credits)  YC – CHE 1213 Organic Chemistry R&L (5 Credits)

 Classical & Quantum Waves (PHYS UN1403)

Met By  SCW – Both Courses Listed Below  PHYS 2051 Waves and Optics (3 credits)  PHYS 2052 Modern Physics (3 credits)

 YC – Both Courses  PHY 2051 Waves and Optics (3 credits)  PHY 2052 Introduction to Modern Physics (3 credits)

 Introduction to Molecular and Cellular Biology (BIOL UN2005)

Met By  SCW - Both Courses o BIOL 3207C Cell Biology (4 credits) o BIOL 3521C Molecular Biology (4 credits)

 YC - Both Courses o BIO 3207C Cell Biology (4 credits) o BIO 3521C Molecular Biology (4 credits)

EARTH AND ENVIRONMENTAL SCIENCES (Chose one of the following 2 and the 3rd  The Climate System (EESC UN2100 ) [may be taken while at Columbia.]  The Solid Earth System (EESC UN2200) [may be taken while at Columbia.]  Better Planet By Design (EAEE E2100) [may be taken while at Columbia.]

There are no current SCW/YC Courses that meet these requirements. They may be taken either before or during enrollment at Columbia.

ELECTRICAL ENGINEERING

MATHEMATICS  Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Introduction to applied mathematics Ordinary Differential Equations & Linear Algebra (APMA E2101). Students who take an ODE course must also take a Linear Algebra course.

COMPUTER SCIENCE Sufficient knowledge of computer programming is needed in order to take Data Structures in Java (W3136) or Data Structures and Algorithms (COMS W3137) at Columbia

Met By

 SCW– COMP 1300 Introduction to Computer Science and Programming (4 credits)  YC – COM 1300 Introduction to Computer Science and Programming (4 credits)

ENGINEERING MECHANICS

MATHEMATICS

 Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Ordinary Differential Equations (APMA E2030).Students who take an ODE course must also take a Linear Algebra course.

Physics  Mechanics (ENME E3105) [may be taken the summer before entering or while at Columbia]

Met By

IEOR:INDUSTRIAL ENGINEERING, ENGINEERING MANAGEMENT SYSTEMS, or OPERATIONS RESEARCH

MATHEMATICS (Note – students who are interested in Financial Engineering must take Differential Equations before coming to Columbia. Students can not apply to this major until after spending one semester at Columbia Engineering.)  Linear Algebra (MATH UN2010 or APAM E3101)

Met By o SCW– MATH 2105 Linear Algebra (3 Credits) o YC – MAT 2105 Linear Algebra (3 Credits)

o The Following courses are substitutes for the Probability and Statistics Requirement.

Met By  SCW – Both Courses o MATH 2461 Probability Theory (3 credits) o MATH 2462 Mathematical Statistics (3 credits)

 YC – Both Courses

o MAT 2461 Probability Theory (3 credits) o MAT 2462 Mathematical Statistics (3 credits)

COMPUTER SCIENCE (choose one language pair – JAVA/PYTHON)  Introduction to Computing for Engineers and Applied Scientists (ENGI E1006) or Introduction to Computer Programming in Java (COMS W1004)  Data Structures in C++ (W3133) or Data Structures in Java (COMS W3134)

Met By  SCW– Three Courses o COMP 1300 Introduction to Computer Science and Programming (PYTHON) (4 credits) o COMP 3650 Object Oriented Programming ---JAVA – (3 credits) o COMP 1320C Introduction to Data Structures (4 credits)  YC – Three Courses o COM 1300 Introduction to Computer Science and Programming (JAVA) (4 credits) o COM 1320 Data Structures (4 credits) o COM 1504 Discrete Structures (PYTHON) (4 credits)

ECONOMICS  Introduction to Accounting and Finance (E2261)

Met By the following two SYMS School of Business courses This course must be taken prior to Columbia or any student with interests in the Financial Engineering major. Students can not apply to this major until after they are already enrolled at Columbia (after the first semester in Columbia Engineering).

 ACC 1001 Accounting Principles I (3 credits)  ACC 1002 Accounting Principles II (3 credits)

MATERIALS SCIENCE AND ENGINEERING

MATHEMATICS  Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 Ordinary Differential Equations (UN20300)

Met By  SCW -- MATH 2601 Differential Equations (3 credits)  YC -- MAT 2601 Differential Equations (3 credits)

PHYSICS  Classical and Quantum Waves (UN1403)

Met By  SCW – Both Courses Listed Below o PHYS 2051 Waves and Optics (3 credits) o PHYS 2052 Modern Physics (3 credits)  YC – both courses below o PHY 2051 Waves and Optics (3 credits) o PHY 2052 Introduction to Modern Physics (3 credits)

CHEMISTRY  General Chemistry I (UN1403) or General Chemistry II II (UN1404)

Met By  SCW– CHEM 1045 or 1046 General Chemistry (4 Credits)  YC – CHE 1045 or 1046 General Chemistry (3 Credits)

 General Chemistry Lab (C1500)

Met By  SCW– CHEM 1045C  YC – CHE 1047L MECHANICAL ENGINEERING

MATHEMATICS  Calculus IV (UN1202) -- this requirement is fulfilled by all candidates after completion of the 3 semester Y.U. Calculus sequence specified in the Foundation Course

 YC– Both Courses o MAT 2601 Differential Equations (3 credits) o MAT 2105 Linear Algebra (3 credits).

PHYSICS/ BIOLOGY (choose one course listed below)  Classical and Quantum Waves (PHYS UN1403)

Met By  SCW – Both Courses Listed Below o PHYS 2051 Waves and Optics (3 credits) o PHYS 2052 Modern Physics (3 credits)  YC – Both courses below o PHY 2051 Waves and Optics (3 credits) o PHY 2052 Introduction to Modern Physics (3 credits)

 Environmental Biology: Elements to Organisms (EEEB UN2001)

Met By  SCW - BIOL 3038C Ecology (4 credits)  YC - BIO 3038C Ecology (4 credits)

 Biochemistry, Genetics, and Molecular Biology (UN2005)

Met By  SCW - Both Courses o BIOL 3207C Cell Biology (4 credits) o BIOL 3521C– Molecular Biology (4 credits)  YC - Both Courses o BIO 3207C Cell Biology (4 credits) o BIO 3521C Molecular Biology (4 credits)

ENGINEERING MECHANICS  Mechanics (ENME E3105) [may be taken while at Columbia]

Met By  SCW – Both Courses must be taken to cover Rigid Bodies o PHYS 1221 Classical Mechanics I (3 credits) o PHYS 1222 Classical Mechanics II (3 credits)  YC – Both Courses must be taken to cover Rigid Bodies o PHY 1221 or 1221H Classical Mechanics (3 credits) o PHY 1222 Advanced Mechanics (3 credits)

ELECTRICAL ENGINEERING  Intro. to Electrical Engineering (ELEN E1201) or equivalent [may be taken while at Columbia]

There is no current SCW/YC Course that meets this requirement.

Appendix I – SCW Courses By Subject

 Biology (BIOL)

BIOL 1011C, 1012C Principles of Biology (4 credits) For majors. Introductory analysis of the various biological concepts at the molecular, cellular, and organismal levels. First semester: biochemistry of molecules, enzyme kinetics, cellular anatomy and physiology, cellular energetics and metabolism, cellular signaling; second semester: cellular reproduction, genetics, molecular biology, population biology, evolution, and comparative human physiology. Laboratory work, including dissections, complements the lectures. (lecture: 3 hours; lab: 3 hours)

BIOL 3038C Ecology (3 credits) An interdisciplinary approach demonstrating the impact of geological, climatological, and evolutionary processes on the distribution of life on earth. Emphasis on the concepts of niche and ecosystem, particularly in laboratory sessions employing living species. Counts toward area 1. Lecture: 2 hours; lab: 4 hours. Laboratory fee. Pre-requisite: BIOL 1012C

BIOL 3207C Cell Biology (4 credits) Basic architecture of cellular organelles and components; dynamics of growth, nutrition, cell cycle, metabolism, and metabolic regulation; specialized cell functions. Laboratory accompanies lectures. Counts toward area 2. Lecture: 2 hours; lab: 4 hours. Laboratory fee. Pre- requisite: BIOL 1012C. Pre- or co-requisite: CHEM 1046C.

BIOL 3521C Molecular Biology (4 credits) A comprehensive study of the gene in prokaryotic and eukaryotic systems. Analysis of the molecular structure of DNA and the chromosome, RNA structure and transcription, RNA processing, translation into proteins, structure and organization of the genes and their regulatory regions, protein-DNA interactions, gene expression mechanisms. Includes a weekly one-hour problem solving recitation.) Prerequisite: BIOL 3207C or BIOL 3513C or CHEM 1376

 Chemistry (CHEM)

CHEM 1045C, CHEM1046C General Chemistry (4 credits) Lecture and laboratory course for students going into the biological, chemical, health, or physical sciences. Atomic structure and stoichiometry; properties of gases, liquids, and solids; thermochemistry; quantum theory; electronic structures of atoms and molecules; chemical bonding; properties of solutions; thermodynamics; chemical equilibria including acidbase and solubility; kinetics; electrochemistry; nuclear chemistry. Laboratory experiments enhance understanding of principles taught in lectures. Emphasis on quantitative techniques; computer interfacing and spreadsheet applications. Second semester includes semi-micro qualitative analysis. Lecture: 3 hours; recitation: 1 hour; lab: 3 hours. Laboratory fee.

CHEM 1213C, CHEM 1214C Organic Chemistry (5,3 credits) The structure, properties, synthesis, and reactions of the main classes of organic compounds, including compounds of biological importance. Principles of stereochemistry, reaction mechanisms, and spectroscopy. Molecular modeling. Laboratory experiments are designed to illustrate methods of separation, purification, identification, and preparation of organic compounds. Llecture: 3 hours; recitation: 1 hour; lab: 4 hours. Laboratory fee. Prerequisite: CHEM 1046C.

 Computer Science (COMP)

COMP 1300C Introduction to Computer Science and Programming (4 credits) Components of a computer system; machine, assembly, and high-level languages; numerical systems and coding; representation of data and instructions; data types, constants, variables; arithmetic expressions; logical expressions; assignment statement; sequencing, alteration, and iteration; arrays, subprograms, and parameters; simple I/O; techniques of problem solving; flowcharting; stepwise refinement; simple numerical examples; basic search and sort algorithms. Principles of good programming style, expression, and documentation; control flow; invariant relation of a loop; stepwise refinement of statements and data structures, or top-down programming. The course uses PYTHON. Lecture: 3 hours; lab: 2 hours. Corequisite: MAT 1412 or the successful completion of a placement test in precalculus mathematics

COMP 1320C Introduction to Data Structures (4 credits) String processing, concatenation, substrings, matching, internal searching and sorting, recursion, linked lists and linear allocation (stacks, queues, deques). Elementary data structures, file structures and algorithms, searching and sorting, trees and algorithms for their manipulation, notions of algorithm complexity, memory and data management systems. Lecture: 3 hours; lab: 2 hours. Prerequisite: COMP 1300

COMP 1504C Discrete Structures (3 credits)

Boolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. Prerequisite: three years of high school mathematics

COMP 1340 Topics: Computational Methods in Scientific Research (3 credits) Use of computers to solve real problems in biology, physical sciences and economics. Numerical methods and data analysis, and how to visualize results with plots and movies. Prerequisites: MATH 1412. Recommended: PHYS 1032C or 1042C. This is also cross-listed as PHYS 1340.

COMP 3650 – Object Oriented Software Design. (3 credits ) Covers Java and its object oriented features in detail, with an emphasis on well-designed object hierarchies. Includes design patterns that exploit encapsulation, polymorphism, inheritance, reusability, and unit testing. Students will be required to implement an object oriented programming project using Java. Prerequisite: COMP 1300

 Economics (ECON)

ECON 1010 Principles of Economics Introduction to microeconomic and macroeconomic analysis. Micro: supply and demand, the behavior of firms and consumers; how markets work; market failures; policy issues such as taxation regulation, and redistribution of income. Macro: General equilibrium, business cycles, inflation, unemployment; national income accounting; monetary and fiscal policy; public debt and social insurance; theories of international trade; long-term growth. (Replaces ECON 1031 and 1041 beginning in Fall 2015.)

 English (ENGL)

ENGL 1100 Composition and Rhetoric (3 credits) Introduction to academic argument and the thesis/claim/evidence form of essay writing, including thesis development, writing process and revision, analytical and research methods.

ENGL 1200H Freshman Honors Seminar (3 credits) Introduction to academic argument and the thesis/claim/evidence form of essay writing, including thesis development, writing process and revision, analytical and research methods. This course is open only to Distinguished Scholars, who substitute it for Composition and Rhetoric. Three hours of lecture plus conferences.

 Math (MATH)

MATH 1412, MATH 1413 Calculus I, II (4 credits each)First semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. Lecture: 3 hours; recitation: 2 hours. Prerequisites: three years of high school mathematics and placement by examination or MATH 1160

MATH 1504 Discrete Structures (3 credits) Boolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. Prerequisite: three years of high school mathematics – Students will have to augment their knowledge with JAVA

MATH 1510 Multivariable Calculus (4 credits)

Limits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minima with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus; theorems of Green, Gauss, and Stokes. Prerequisite: MATH 1413.

MATH 2105 Linear Algebra I (3 credits) THE MATH DEPARTMENT HAS RECENTLY CONSOLIDATED THIS TO ONE COURSE.Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors, diagonalization; quadratic forms; canonical forms; spectral theory; applications. Prerequisite: MAT 1412

MATH 2461 Probability Theory (3 credits) Discrete and continuous sample spaces; combinatorial analysis; density and distribution functions of random variables; expectation and variance; independence and conditional probability; law of large numbers; central limit theorem; generating functions; random walk and ruin problems. Prerequisite: MATH 1510.

MATH 2462 Mathematical Statistics (3 credits) Application of probability theory to the classical parametric models: moment-generating functions, chi-square and t distributions, central limit theorem, sampling distributions, maximum likelihood and interval estimation, confidence intervals, hypothesis testing; nonparametric models; the Bayesian controversy. Examples from natural science and social and behavioral research. Prerequisite: MATH 2461

MATH 2601 Differential Equations (3 credits) Classification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite: MATH 1413

 Physics (PHYS)

PHYS 1041C, 1042C General Physics (5 credits) PHYS 1041C, 1042C General Physics (5 credits) Two-semester, calculus-based course for Physics, Physical Sciences and Pre-Engineering majors. Topics covered: kinematics and dynamics of the particle and rigid bodies, conservation laws, momentum, energy and angular momentum, oscillations, waves, fluids, electromagnetism and optics. Laboratory experiments are designed to help students master the principles covered in lecture. Lecture: 4 hours; recitation: 1 hour; lab: 2 hours 45 minutes. Laboratory fee. Prerequisite for PHYS 1041C: MATH 1412 or more advanced or instructors permission. Prerequisite or corequisite for PHYS 1042C: MATH 141. Prerequisite or co-requisite for PHYS 1042C: MATH 1413

PHYS 2051 Intermediate Physics I 3 credits This course examines wave phenomena with an emphasis on light and offers an introduction to thermal physics. Topics covered include mechanical waves, sound, light as an electromagnetic wave, geometrical optics, interference, diffraction, temperature, heat and the laws of thermodynamics. Prerequisites: PHYS 1042, MATH 1413. Co-requisite: MATH 1510.

2052 Intermediate Physics II 3 credits This course introduces the main ideas of modern physics as they were historically developed during the great revolution that took place in Physics between 1880 and 1930, which shaped our current ideas in relativity, quantum mechanics and statistical physics. It presents in a historical context how those ideas were generated, which were the great experiments that led to their development, and the theoretical underpinnings on which they rest. Prerequisite: PHYS 2051

PHYS 1221 Classical Mechanics I (3 credits) Newtonian mechanics; oscillations: simple, damped and driven; resonance; elements of nonlinearity; non-inertial frames of reference; motion relative to the Earth; conservative forces and potential energy; central forces; planetary motion. Prerequisite or corequisite: PHYS 1041C.

PHYS 1222 Classical Mechanics II (3 credits) Lagrangian mechanics. Constraints. Variational calculus and Hamilton's equations. Rotations of rigid bodies in two and three dimensions. Eulers equations. Tensor analysis. Small coupled oscillations and normal coordinates. Classical waves: the wave equation, dispersion, interference, polarization. Fresnel and Fraunhofer diffraction. Prerequisite PHYS1221.

PHYS 1340 Topics: Computational Methods in Scientific Research (3 credits) Use of computers to solve real problems in biology, physical sciences and economics. Numerical methods and data analysis, and how to visualize results with plots and movies. Prerequisites: MATH 1412. Recommended: PHYS 1032C or 1042C. This is also cross-listed as COMP 1340.

Appendix II – YC Courses By Subject

 Biology (BIO)

BIO 1011R, 1012R Principles of Biology—Lectures (3 credits) Introduction to the study of living organisms, including such areas as the structure and function of living things, ecology, role of plants in nature, energy cycles, reproduction, heredity, and evolution. The human organism, including normal and abnormal structure and function. Corequisite: BIO 1011L, 1012L.

BIO 3038C Ecology (4 credits) Classical ecological approaches in light of recent ecological discoveries. An interdisciplinary approach demonstrating the relationships of geological, climatological, and evolutionary principles to ecology. Laboratory work and field trips accompany lectures. Lecture: 2 hours; lab: 4 hours. Laboratory fee. Prerequisite: BIO 1012

BIO 3207C Cell Biology (4 credits) Basic architecture of cells, organelles, and components; dynamics of growth, nutrition, cell cycle, metabolism, and metabolic regulation; specialized cell functions. Laboratory accompanies lectures.Lecture: 2 hours; lab: 4 hours. Laboratory fee. Prerequisites: BIO 1012, CHE 1046

BIO 3521C Molecular Biology (4 credits) Recombinant DNA techniques and applications. Special attention to recently published journal articles. Laboratory accompanies lectures. Lecture: 2 hours; lab: 4 hours. Laboratory fee. Prerequisite: BIO 1012

 Chemistry (CHE)

CHE 1045R, 1046R General Chemistry I & II (Lecture) (3,3 credits) This two course sequence explores the fundamental concepts of chemistry on both the atomic and macroscopic scales. Topics include atomic structure and stoichiometry; properties of gases, liquids, and solids; thermochemistry; quantum theory and the electronic structure of atoms; the periodic table and periodic properties; chemical bonding and molecular orbital theory; properties of solutions; thermodynamics; acidbase and solubility equilibria; chemical kinetics; electrochemistry; and nuclear chemistry. Corequisite: CHE 1045L, 1046L.

CHE 1047LGeneral Chemistry (Lab) (2 credits) Laboratory experiments are designed and scheduled to complement lecture topics and enhance students understanding of the principles introduced. Emphasis on quantitative techniques. Prerequisite: For students in the combined pre-engineering program who only need one semester of Chemistry lab and lecture, the following exception will be made: CHE 1045R will be considered a pre-requisite for CHE 1047L as opposed to the regular requisite requirement.

CHE 1213R, 1214R Organic Chemistry I & II (Lecture) (3,3 credits) Organic chemistry explores the rich chemistry of carbon. Topics include the structure, synthesis, properties, and reaction mechanisms of the main classes of organic compounds, including compounds of biological importance. Prerequisite: CHE 1046R&L/H. Corequisite: CHE 1213L, 1214L

CHE 1215L Organic Chemistry I (Lab) (2 credits) Emphasizes basic techniques in separation, purification, identification and preparation of organic compounds. Prerequisite: CHE 1046R, CHE 1047L. Corequisite: CHE 1213R

 Computer Science (COM)

COM 1300C Introduction to Computer Science and Programming (4 credits) Components of a computer system; machine, assembly, and high-level languages; numerical systems and coding; representation of data and instructions; data types, constants, variables; arithmetic expressions; logical expressions; assignment statement; sequencing, alteration, and iteration; arrays, subprograms, and parameters; simple I/O; techniques of problem solving; flowcharting; stepwise refinement; simple numerical examples; basic search and sort algorithms. Principles of good programming style, expression, and documentation; control flow; invariant relation of a loop; stepwise refinement of statements and data structures, or top-down programming. The course uses JAVA. [Students are expected to learn C++ for later courses]Lecture: 3 hours; lab: 2 hours. Corequisite: MAT 1412 or the successful completion of a placement test in precalculus mathematics

COM 1320 Data Structures (4 credits) String processing, concatenation, substrings, matching, internal searching and sorting, recursion, linked lists and linear allocation (stacks, queues, deques). Elementary data structures, file structures and algorithms, searching and sorting, trees and algorithms for their manipulation, notions of algorithm complexity, memory and data management systems. Lecture: 3 hours; lab: 2 hours.Prerequisite: COM 1300. Corequisite: COM 1504

COM 1504 Discrete Structures (4 credits) Boolean algebra and predicate calculus; proof methods; sets, functions and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. This course uses PYTHON. Lecture: 3 hours; lab: 2 hours. Prerequisite: three years of high school mathematics.

 Economics (ECO)

ECO 1010 Principles of Economics Introduction to microeconomic and macroeconomic analysis. Micro: supply and demand, the behavior of firms and consumers; how markets work; market failures; policy issues such as taxation regulation, and redistribution of income. Macro: General equilibrium, business cycles, inflation, unemployment; national income accounting; monetary and fiscal policy; public debt and social insurance; theories of international trade; long-term growth. (Replaces ECON 1031 and 1041 beginning in Fall 2015.).

 English (ENG)

ENG 1020 First Year Writing (3 credits) First Year Writing introduces students to college-level writing and prepares them for other academic work by deepening reading comprehension and critical thinking skills. This course emphasizes the writing process so that students can develop strategies for invention, exploration, and revision. First Year Writing encourages rhetorical flexibility and helps students integrate and build on sources in order to consider topics from different viewpoints, gain more knowledge, and learn how to cite others’ words and ideas according to academic documentation practices.

 Math (MAT)

MAT 1412, MATH 1413 Calculus I, II (4 credits each) First semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. Lecture: 3 hours; recitation: 2 hours. Prerequisites: three years of high school mathematics and placement by examination or MAT 1160

MAT 1510 Multivariable Calculus (4 credits) Limits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minima with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus; theorems of Green, Gauss, and Stokes. Prerequisite: MAT 1413.

MAT 2105 Linear Algebra (3 credits)

Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors, diagonalization; quadratic forms; canonical forms; spectral theory; applications. Prerequisite: MAT 1412.

MAT 2461 Probability Theory (3 credits) Probability spaces; combinatorics; conditional probability; discrete and continuous random variables; examples; density and distribution functions; independence; expectation and variance; multivariate distributions; moment-generating functions; applications. Prerequisite: MAT 1510.

MAT 2462 Mathematical Statistics (3 credits) Functions of random variables; Central Limit Theorem; chi-square distribution; t-distribution; F-distribution; point and interval estimation; maximum likelihood; hypothesis testing; analysis of variance. Prerequisite: MAT 2461

MAT 2601 Differential Equations (3 credits) Classification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite: MAT 1413

 Physics (PHY)

PHY 1051R General Physics—Lectures (4 credits) The course will focus on the motions of bodies from billiard balls along a table top to carts sliding down inclined planes to planets revolving about our Sun.Such motions will be described through the framework of Newtonian mechanics.Newton’s laws of motion allow one to predict the future motion of an object given thepresent state of circumstances. A large class of classical phenomena is to be investigated.Topics to be discussed include measurements, motion along a straight line, vectores,motion in two and three dimensions, Newton’s laws, Applications of Newton’s laws toeveryday problems, Kinetic Energy and Work, Potential Energy and Energyconservation, Center of mass and Linear momentum, Rotation, Rolling, torque andangular momentum, Equilibrium and elasticity, and, finally, Gravitation and planetarymotion. Fluid Mechanics. Lecture: 4 hours; Recitation: 1 hour. Prerequisite: MAT 1412. Corequisite:

PHY 1052R General Physics—Lectures (4 credits) This course will be offered as the second semester of general physics. It focuses starts with waves and focuses on electricity and magnetism, whichincludes electric fields, magnetic fields, electromagnetic forces, conductors and dielectrics, electromagnetic waves, and the nature of light. Lecture: 4 hours; Recitation: 1 hour. Corequisite: Math 1413, Physics 1061L

PHY 1061L, 2061L General Physics— Laboratory (1 credit) Laboratory experiments designed to complement the principles covered in PHY 1041R–1042R. Covers mechanics, heat, optics, elasticity, electricity, circuits, and magnetism. (2 hours) Laboratory fee: $40. Corequisite: PHY 1041R, PHY 1042R

PHY 2051 Waves and Optics (3 credits) I This course examines wave phenomena with an emphasis on light and offers an introduction to thermal physics. Topics covered include mechanical waves, sound, light as an electromagnetic wave, geometrical optics, interference, diffraction, temperature, heat and the laws of thermodynamics. Prerequisites: PHY 1052, MAT 1413. Co-requisite: MATH 1510, PHY 2061L.

PHY 2052 Introduction to Modern Physics (3 credits) This course introduces the main ideas of modern physics as they were historically developed during the great revolution that took place in Physics between 1880 and 1930, which shaped our current ideas in relativity, quantum mechanics and statistical physics. It presents in a historical context how those ideas were generated, which were the great experiments that led to their development, and the theoretical underpinnings on which they rest.| Prerequisites: PHY 1051, PHY 1052

PHY 1221 or 1221H Classical Mechanics (3 credits) Particle motion in space, time, or velocity-dependent potentials. Damped and driven oscillations, resonances. Elements of nonlinearity and chaos. Noninertial reference systems. Motion relative to the Earth. Central forces. Planetary motion. Stability of orbits. Prerequisites: PHY 1041, PHY 1042. Corequisite: MAT 1510.

PHY 1222 Advanced Mechanics (3 credits) Systems of particles. Variable mass. Collision theory. Lagrangian mechanics. Constraints. Variational calculus and Hamilton’s equations. Rotations of rigid bodies in two and three dimensions. Euler’s equations. Tensor analysis. Small coupled oscillations and normal coordinates. Fluid mechanics. Viscosity. Relativistic mechanics. Prerequisites: PHY 1041, PHY 1042, MAT 1510 Recommended: MAT 2105, PHY 1221.

PHY 3301 or 3301H Computational Methods in the Physical Sciences (3 credits) Basic use of symbolic logic software and exploration of different areas of physics through numerical and computational techniques, including random-walk models, accretion phenomena, Monte Carlo methods in statistical physics, cellular automata, complexity, chaos, and planetary motion. Methods of interpolation, rates of convergence, projection methods, boundary problems and singular perturbation methods. Prerequisites: PHY 1041, PHY 1042. Recommended: COM 1300.

Appendix III – SYMS School of Business Courses By Subject

 Accounting (ACC)

ACC 1001 Accounting Principles I (3 credits) Introduction to financial accounting: the accounting cycle, preparation of financial statements, accounting for cash and temporary investments, receivables, inventories, and long-lived assets.

ACC 1002 Accounting Principles II (3 credits) Accounting for current and long-term liabilities, stockholders' equity, statement of cash flows, introduction to management accounting, cost behavior, and break-even analysis.