Electrical Engineering (BS)
The educational objective of the Electrical Engineering program, in support of the mission of the School, is to prepare graduates to achieve success in one or more of the following within a few years after graduation:
- Graduate or professional studies—as evidenced by admission to a top-tier program, attainment of advanced degrees, research contributions, or professional recognition.
- Engineering practice—as evidenced by entrepreneurship; employment in industry, government, academia, or nonprofit organizations in engineering; patents; or professional recognition.
- Careers outside of engineering that take advantage of an engineering education—as evidenced by contributions appropriate to the chosen field.
The Electrical Engineering program will prepare its undergraduates to attain the following:
- an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
- an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors
- an ability to communicate effectively with a range of audiences
- an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts
- an ability to function effectively on teams whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives
- an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions
- an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
The B.S. program in electrical engineering at Columbia University seeks to provide a broad and solid foundation in the current theory and practice of electrical engineering, including familiarity with basic tools of math and science, an ability to communicate ideas, and a humanities background sufficient to understand the social implications of engineering practice. Graduates should be qualified to enter the profession of engineering, to continue toward a career in engineering research, or to enter other fields in which engineering knowledge is essential. Required nontechnical courses cover civilization and culture, philosophy, economics, and a number of additional electives. English communication skills are an important aspect of these courses. Required science courses cover basic chemistry and physics, whereas math requirements cover calculus, differential equations, probability, and linear algebra. Basic computer knowledge is also included, with an introductory course on using engineering workstations and two rigorous introductory computer science courses. Core electrical engineering courses cover the main components of modern electrical engineering and illustrate basic engineering principles. Topics include a sequence of two courses on circuit theory and electronic circuits, one course on semiconductor devices, one on electromagnetics, one on signals and systems, one on digital systems, and one on communications or networking. Engineering practice is developed further through a sequence of laboratory courses, starting with a first-year course to introduce hands-on experience early and to motivate theoretical work. Simple creative design experiences start immediately in this first-year course. Following this is a sequence of lab courses that parallel the core lecture courses. Opportunities for exploring design can be found both within these lab courses and in the parallel lecture courses, often coupled with experimentation and computer simulation, respectively. The culmination of the laboratory sequence and the design experiences introduced throughout earlier courses is a senior design course (capstone design course), which includes a significant design project that ties together the core program, encourages creativity, explores practical aspects of engineering practice, and provides additional experience with communication skills in an engineering context. Finally, several technical electives are required, chosen to provide both breadth and depth in a specific area of interest. More detailed program objectives and outcomes are posted at ee.columbia.edu.
The program in electrical engineering leading to the B.S. degree is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org.
There is a strong interaction between the Department of Electrical Engineering and the Departments of Computer Science, Applied Physics and Applied Mathematics, Industrial Engineering and Operations Research, Physics, and Chemistry.
EE Core Curriculum
All electrical engineering (EE) students must take a set of core courses, which collectively provide the student with fundamental skills, expose them to the breadth of EE, and serve as a springboard for more advanced work, or for work in areas not covered in the core. These courses are shown on the charts in Undergraduate Degree Tracks. A full curriculum checklist is also posted at ee.columbia.edu.
Technical Electives
The 18-point technical elective requirement for the electrical engineering program consists of three components: depth, breadth, and other. A general outline is provided here, and more specific course restrictions can be found at ee.columbia.edu. For any course not clearly listed there, adviser approval is necessary.
The depth component must consist of at least 6 points of electrical engineering courses in one of four defined areas:
- photonics, solid-state devices, and electromagnetics;
- circuits and electronics;
- signals and systems; and
- communications and networking.
The depth requirement provides an opportunity to pursue particular interests and exposure to the process of exploring a discipline in depth—an essential process that can be applied later to other disciplines, if desired.
The breadth component must consist of at least 6 additional points of courses that are outside of the chosen depth area and have significant engineering content. These courses can be from other departments within the School. The breadth requirement precludes overspecialization. Breadth is particularly important today, as innovation requires more and more of an interdisciplinary approach, and exposure to other fields is known to help one’s creativity in one’s own main field. Breadth also reduces the chance of obsolescence as technology changes.
Any remaining technical elective courses, beyond the minimum 12 points of depth and breadth, do not have to be engineering courses (except for students without ELEN E1201 INTRO-ELECTRICAL ENGINEERING or approved transfer credit for ELEN E1201 INTRO-ELECTRICAL ENGINEERING) but must be technical. Generally, math and science courses that do not overlap with courses used to fill other requirements are allowed.
If another department advertises that one of their courses can be used as a technical elective, that does not necessarily mean it will be approved as a technical elective in the electrical engineering program. Which courses are approved depends on other electives chosen due to the depth and breadth restrictions, and the need for sufficient engineering and technical content within the entire 18 points. Electrical engineering technical electives must also be 3000 level or above and must not have significant overlap with other courses taken for the major.
Starting Early
The EE curriculum is designed to allow students to start their study of EE in their first year. This motivates students early and allows them to spread nontechnical requirements more evenly. It also makes evident the need for advanced math and physics concepts, and motivates the study of such concepts. Finally, it allows more time for students to take classes in a chosen depth area, or gives them more time to explore before choosing a depth area. Students can start with ELEN E1201 INTRO-ELECTRICAL ENGINEERING in the second semester of their first year, and can continue with other core courses one semester after that, as shown in the “early-starting students” chart. It is emphasized that both the early- and late-starting sample programs shown in the charts are examples only; schedules may vary depending on student preparation and interests.
Transfer Students
Transfer students coming to Columbia as juniors with sufficient general background can complete all requirements for the B.S. degree in electrical engineering. Such students fall into one of two categories:
Plan 1: Students coming to Columbia without having taken the equivalent of ELEN E1201 INTRO-ELECTRICAL ENGINEERING must take this course in their junior year. This requires postponing the core courses in circuits and electronics until the senior year, and thus does not allow taking electives in that area; thus, such students cannot choose circuits and electronics as a depth area.
Plan 2: This plan is for students who have taken a course equivalent to ELEN E1201 INTRO-ELECTRICAL ENGINEERING at their school of origin, including a laboratory component. Many pre-engineering programs and physics departments at four-year colleges offer such courses. Such students can start taking circuits at Columbia immediately, and thus can choose circuits and electronics as a depth area.
It is stressed that ELEN E1201 INTRO-ELECTRICAL ENGINEERING or its equivalent is a key part of the EE curriculum. The preparation provided by this course is essential for a number of other core courses.
Sample programs for both Plan 1 and Plan 2 transfer students can be found at ee.columbia.edu.
Electrical Engineering Program
An overview of the degree track in PDF format can be found here.
Early-Starting Students
First Year | ||
---|---|---|
Semester I | ||
MATH UN1101 | CALCULUS I | |
Choose one of the following Physics courses depending on track: | ||
INTRO TO MECHANICS ＆ THERMO | ||
PHYSICS I:MECHANICS/RELATIVITY | ||
ACCELERATED PHYSICS I | ||
Choose a one-semester Chemistry lecture: | ||
GENERAL CHEMISTRY I-LECTURES | ||
GENERAL CHEMISTRY II-LECTURES | ||
INTENSVE ORGANIC CHEMISTRY | ||
2ND TERM GEN CHEM (INTENSIVE) | ||
ELEN E1201 (taken Semester l or ll) | INTRO-ELECTRICAL ENGINEERING | |
ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTERPIECS I | ||
CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
HUMA UN1121 or UN1123 (taken Semester l, ll, lll, or lV) | MASTERPIECES OF WESTERN ART | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTRPIECS II | ||
CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
ECON UN1105 - ECON UN1155 (taken Semester l, ll, lll, or lV) | PRINCIPLES OF ECONOMICS | |
ENGI E1006 (taken Semester l or ll)^{1} | INTRO TO COMP FOR ENG/APP SCI | |
PHED UN1001 | PHYSICAL EDUCATION ACTIVITIES | |
ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
Semester II | ||
MATH UN1102 | CALCULUS II | |
Choose one of the following Physics courses depending on track: | ||
INTRO ELEC/MAGNETSM ＆ OPTCS | ||
PHYSICS II: THERMO, ELEC ＆ MAG | ||
ACCELERATED PHYSICS II | ||
ELEN E1201 (taken Semester l or ll) | INTRO-ELECTRICAL ENGINEERING | |
ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTERPIECS I | ||
CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
HUMA UN1121 or UN1123 (taken Semester l, ll, lll, or lV) | MASTERPIECES OF WESTERN ART | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTRPIECS II | ||
CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
ECON UN1105 - ECON UN1155 (taken Semester l, ll, lll, or lV) | PRINCIPLES OF ECONOMICS | |
ENGI E1006 (taken Semester l or ll)^{1} | INTRO TO COMP FOR ENG/APP SCI | |
PHED UN1002 | PHYSICAL EDUCATION ACTIVITIES | |
ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
Second Year | ||
Semester III | ||
APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
ELEN E3201 | CIRCUIT ANALYSIS | |
ELEN E3801 | SIGNALS AND SYSTEMS | |
ELEN E3081^{2} | CIRCUIT ANALYSIS LABORATORY | |
ELEN E3084^{2} | SIGNALS ＆ SYSTEMS LABORATORY | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTERPIECS I | ||
CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
HUMA UN1121 or UN1123 (taken Semester l, ll, lll, or lV) | MASTERPIECES OF WESTERN ART | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTRPIECS II | ||
CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
ECON UN1105 - ECON UN1155 (taken Semester l, ll, lll, or lV) | PRINCIPLES OF ECONOMICS | |
Semester IV | ||
APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
APMA E2101^{3} | INTRO TO APPLIED MATHEMATICS | |
ELEN E3331 | ELECTRONIC CIRCUITS | |
CSEE W3827 | FUNDAMENTALS OF COMPUTER SYSTS | |
ELEN E3083^{2} | ELECTRONIC CIRCUITS LABORATORY | |
ELEN E3082^{2} | DIGITAL SYSTEMS LABORATORY | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
EURPN LIT-PHILOS MASTERPIECS I | ||
CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
HUMA UN1121 or UN1123 (taken Semester l, ll, lll, or lV) | MASTERPIECES OF WESTERN ART | |
Choose one of the following Required Nontechnical Electives (taken Semester l, ll, lll, or lV): | ||
HUMA CC1002 | EURPN LIT-PHILOS MASTRPIECS II | |
COCI CC1102 | CONTEMP WESTRN CIVILIZATION II | |
Global Core (3–4) | ||
ECON UN1105 - ECON UN1155 | PRINCIPLES OF ECONOMICS | |
Third Year | ||
Semester V | ||
Choose one of the following Physics courses depending on track: | ||
INTRO-CLASSCL ＆ QUANTUM WAVES | ||
PHYSICS III:CLASS/QUANTUM WAVE | ||
PHYS UN3081 | INTERMEDIATE LABORATORY WORK | |
ELEN E3106 | SOLID STATE DEVICES-MATERIALS | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{4} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{5} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{6} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) | ||
Semester VI | ||
PHYS UN1494 (choose this Physics course depending on track)^{9} | INTRO TO EXPERIMENTAL PHYS-LAB | |
ELEN E3401 | ELECTROMAGNETICS | |
ELEN E3701 or CSEE W4119^{10} | INTRO TO COMMUNICATION SYSTEMS | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{4} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{5} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{6} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) | ||
Fourth Year | ||
Semester VII | ||
ELEN E3043 | SOLID ST,MICROWAVE,FBR OPT LAB | |
ELEN E3399 | ELECTRICAL ENGINEERING PRACTICE | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{4} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{5} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{6} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) | ||
Semester VIII | ||
ELEN E3390^{11} | EE SENIOR DESIGN PROJECT | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{4} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{5} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{6} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) |
- ^{ 1 }
ENGI E1006 INTRO TO COMP FOR ENG/APP SCI may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences.
- ^{ 2 }
If possible, these labs should be taken along with their corresponding lecture courses.
- ^{ 3 }
APMA E2101 INTRO TO APPLIED MATHEMATICS may be replaced by MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS (formerly MATH E1210) and either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA.
- ^{ 4 }
Some of these courses are not offered both semesters. Students with an adequate background can take some of these courses in the sophomore year.
SIEO W3600 INTRO PROBABILITY/STATISTICS and STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS cannot generally be used to replace IEOR E3658 PROBABILITY FOR ENGINEERS or STAT GU4203 PROBABILITY THEORY.
- ^{ 5 }
Some of these courses are not offered both semesters. Students with an adequate background can take some of these courses in the sophomore year.
Students who plan to minor in Computer Science should choose COMS W3134 Data Structures in Java or COMS W3137 HONORS DATA STRUCTURES ＆ ALGOL
- ^{ 6 }
For details, see ee.columbia.edu
- ^{ 7 }
See ee.columbia.edu
- ^{ 8 }
Consisting of more depth or breadth courses, or further options listed at ee.columbia.edu/ee-undergraduate-program.
The total points of technical electives is reduced to 15 if APMA E2101 INTRO TO APPLIED MATHEMATICS has been replaced by MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS (formerly MATH E1210) and either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can also apply for this waiver, but the courses must have been at an advanced level for this to be considered.
- ^{ 9 }
Chemistry lab (CHEM UN1500 GENERAL CHEMISTRY LABORATORY) may be substituted for physics lab, although this is not generally recommended.
- ^{ 10 }
These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied.
- ^{ 11 }
The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. If special arrangements are made in ELEN E3399 ELECTRICAL ENGINEERING PRACTICE, it is possible to use courses such as ELEN E3998 PROJECTS IN ELEC ENGINEERING, ELEN E4350 VLSI design laboratory, ELEN E4998 INTERMEDIATE PROJECTS, EECS E4340 COMPUTER HARDWARE DESIGN, or CSEE W4840 EMBEDDED SYSTEMS in place of ELEN E3390 EE SENIOR DESIGN PROJECT.
Electrical Engineering Program
Late-Starting Students
First Year | ||
---|---|---|
Semester I | ||
MATH UN1101 | CALCULUS I | |
Choose one of the following Physics courses depending on track: | ||
INTRO TO MECHANICS ＆ THERMO | ||
PHYSICS I:MECHANICS/RELATIVITY | ||
ACCELERATED PHYSICS I | ||
Choose a one-semester Chemistry lecture: | ||
GENERAL CHEMISTRY I-LECTURES | ||
GENERAL CHEMISTRY II-LECTURES | ||
INTENSVE ORGANIC CHEMISTRY | ||
2ND TERM GEN CHEM (INTENSIVE) | ||
ELEN E1201 (taken Semester l or ll)^{1} | INTRO-ELECTRICAL ENGINEERING | |
ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
ENGI E1006 (taken Semester l, ll, lll, or lV)^{2} | INTRO TO COMP FOR ENG/APP SCI | |
PHED UN1001 | PHYSICAL EDUCATION ACTIVITIES | |
ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
Semester II | ||
MATH UN1102 | CALCULUS II | |
Choose one of the following Physics courses depending on track: | ||
INTRO ELEC/MAGNETSM ＆ OPTCS | ||
PHYSICS II: THERMO, ELEC ＆ MAG | ||
ACCELERATED PHYSICS II | ||
ELEN E1201 (taken Semester l or ll)^{1} | INTRO-ELECTRICAL ENGINEERING | |
ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
ENGI E1006 (taken Semester l, ll, lll, or lV)^{2} | INTRO TO COMP FOR ENG/APP SCI | |
PHED UN1002 | PHYSICAL EDUCATION ACTIVITIES | |
ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
Second Year | ||
Semester III | ||
APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
Choose one of the following Physics courses depending on track: | ||
INTRO-CLASSCL ＆ QUANTUM WAVES | ||
PHYSICS III:CLASS/QUANTUM WAVE | ||
INTERMEDIATE LABORATORY WORK | ||
Choose one of the following Required Nontechnical Electives: | ||
EURPN LIT-PHILOS MASTERPIECS I | ||
CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
HUMA UN1121 or UN1123 | MASTERPIECES OF WESTERN ART | |
ENGI E1006 (taken Semester l, ll, lll, or lV)^{2} | INTRO TO COMP FOR ENG/APP SCI | |
Semester IV | ||
APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
APMA E2101^{3} | INTRO TO APPLIED MATHEMATICS | |
PHYS UN1494 (choose this Physics course depending on track)^{4} | INTRO TO EXPERIMENTAL PHYS-LAB | |
Choose one of the following Required Nontechnical Electives: | ||
EURPN LIT-PHILOS MASTRPIECS II | ||
CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
ECON UN1105 - ECON UN1155 | PRINCIPLES OF ECONOMICS | |
ENGI E1006 (taken Semester l, ll, lll, or lV)^{2} | INTRO TO COMP FOR ENG/APP SCI | |
Third Year | ||
Semester V | ||
ELEN E3106 | SOLID STATE DEVICES-MATERIALS | |
ELEN E3201 | CIRCUIT ANALYSIS | |
ELEN E3801 | SIGNALS AND SYSTEMS | |
ELEN E3081^{5} | CIRCUIT ANALYSIS LABORATORY | |
ELEN E3084^{5} | SIGNALS ＆ SYSTEMS LABORATORY | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{6} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{9} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{10} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) | ||
Semester VI | ||
CSEE W3827 | FUNDAMENTALS OF COMPUTER SYSTS | |
ELEN E3331 | ELECTRONIC CIRCUITS | |
ELEN E3401 | ELECTROMAGNETICS | |
ELEN E3701 or CSEE W4119 | INTRO TO COMMUNICATION SYSTEMS | |
ELEN E3083^{5} | ELECTRONIC CIRCUITS LABORATORY | |
ELEN E3082^{5} | DIGITAL SYSTEMS LABORATORY | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{6} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{9} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{10} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) | ||
Fourth Year | ||
Semester VII | ||
ELEN E3043 | SOLID ST,MICROWAVE,FBR OPT LAB | |
ELEN E3399 | ELECTRICAL ENGINEERING PRACTICE | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{6} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll)^{8} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{9} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{10} | ||
Nontech Electives: Complete 27-point requirement; taken Semester V, Vl, Vll, or Vlll) | ||
Semester VIII | ||
ELEN E3390^{11} | EE SENIOR DESIGN PROJECT | |
IEOR E3658 or STAT GU4203 (taken Semester V, Vl, Vll, or Vlll)^{6} | PROBABILITY FOR ENGINEERS | |
Choose one of the following Other Required Courses (taken Semester V, Vl, Vll, or Vlll):^{7} | ||
ESSENTIAL DATA STRUCTURES | ||
Data Structures in Java | ||
HONORS DATA STRUCTURES ＆ ALGOL | ||
EE Depth Tech Electives: At least two technical electives in one depth area. (taken Semester V, Vl, Vll, or Vlll) ^{8} | ||
The four depth areas are: | ||
(a) photonics, solid-state devices, and electromagnetics; | ||
(b) circuits and electronics; | ||
(c) signals and systems; | ||
(d) communications and networking | ||
Breadth Tech Electives (at least 6 points total) (taken Semester V, Vl, Vll, or Vlll):^{9} | ||
At least two technical electives outside the chosen depth area; must be courses with significant engineering content | ||
Other Tech Electives: Additional technical electives as required to bring the total points of technical electives to 18 (taken Semester V, Vl, Vll, or Vlll)^{10} | ||
Nontech Electives: Complete 27-point requirement (taken Semester V, Vl, Vll, or Vlll) |
- ^{ 1 }
Transfer students and 3-2 Combined Plan students who have not taken ELEN E1201 INTRO-ELECTRICAL ENGINEERING prior to the junior year are expected to have taken a roughly equivalent course when they start ELEN E3201 CIRCUIT ANALYSIS.
- ^{ 2 }
ENGI E1006 INTRO TO COMP FOR ENG/APP SCI may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences.
- ^{ 3 }
APMA E2101 INTRO TO APPLIED MATHEMATICS may be replaced by MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS (formerly MATH E1210) and either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA.
- ^{ 4 }
Chemistry lab (CHEM UN1500 GENERAL CHEMISTRY LABORATORY) may be substituted for physics lab, although this is not generally recommended.
- ^{ 5 }
If possible, these labs should be taken along with their corresponding lecture courses.
- ^{ 6 }
Some of these courses are not offered both semesters. Students with an adequate background can take some of these courses in the sophomore year.
SIEO W3600 INTRO PROBABILITY/STATISTICS and STAT GU4001 INTRODUCTION TO PROBABILITY AND STATISTICS cannot generally be used to replace IEOR E3658 PROBABILITY FOR ENGINEERS or STAT GU4203 PROBABILITY THEORY
- ^{ 7 }
Some of these courses are not offered both semesters. Students with an adequate background can take some of these courses in the sophomore year.
Students who plan to minor in Computer Science should choose COMS W3134 Data Structures in Java or COMS W3137 HONORS DATA STRUCTURES ＆ ALGOL.
- ^{ 8 }
For details, see ee.columbia.edu.
- ^{ 9 }
See ee.columbia.edu
- ^{ 10 }
Consisting of more depth or breadth courses, or further options listed at ee.columbia.edu/ee-undergraduate-program.
The total points of technical electives is reduced to 15 if APMA E2101 INTRO TO APPLIED MATHEMATICS has been replaced by MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS (formerly MATH E1210) and either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can also apply for this waiver, but the courses must have been at an advanced level for this to be considered.
- ^{ 11 }
The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. If special arrangements are made in ELEN E3399 ELECTRICAL ENGINEERING PRACTICE, it is possible to use courses such as ELEN E3998 PROJECTS IN ELEC ENGINEERING, ELEN E4350 VLSI design laboratory, ELEN E4998 INTERMEDIATE PROJECTS, EECS E4340 COMPUTER HARDWARE DESIGN, or CSEE W4840 EMBEDDED SYSTEMS in place of ELEN E3390 EE SENIOR DESIGN PROJECT.
Note: This chart shows one possible schedule for a student who takes most of their major program in the final two years. Please refer to the previous chart for a recommended earlier start.