Master's Self-Study

Electrical Engineering

A master's level core: circuits, signals, systems and control, devices, digital systems, communications, electromagnetics, power, and optimization, ending in a design project.

Orientation

Ivy League and Stanford EE master's degrees are built from depth plus breadth, not a fixed core. Stanford's MS asks for 12 units of depth in one area, 9 units of breadth, and 15 technical units (45 total, no thesis). Columbia's MS is 30 points with at least 15 at the 6000 level. Penn's MSE asks for 5 core units spread across physical devices, circuits and computer engineering, and information and decision systems. Cornell's and Dartmouth's M.Eng. degrees add a design project; Princeton's M.Eng. is eight technical courses.

This program gives you that breadth in 14 weeks using the courses those departments have opened to the public (Stanford Engineering Everywhere, MIT OpenCourseWare, which is not an Ivy but is the standard open reference), then asks you to choose one depth area for the capstone.

Realistic expectation: a real MS takes 1.5 to 2 years full time. Treat each module as an orientation to one graduate course, and use the linked full course to go deeper in your chosen area.

Prerequisites

  • Math (required): single and multivariable calculus, linear algebra (matrices, eigenvalues), ordinary differential equations, complex numbers, and basic probability. Module 1 is a diagnostic and bootcamp; if it takes you more than a week, take 18.06 and 18.03 in full first.
  • Physics: calculus-based electricity and magnetism (OpenStax University Physics Volume 2 is enough).
  • Programming: Python with NumPy and Matplotlib (or GNU Octave). Every module has a computational exercise.
  • Hardware (optional but recommended): a breadboard kit, a multimeter, and a low-cost USB oscilloscope for the lab exercises. Buying anything is your call; all exercises also work in simulation.

Pace: 14 weeks at about 12 to 15 hours a week. Graduate EE courses assume 10 or more hours per course per week.

What the schools teach

StanfordMS: 45 units; 12 units depth in one area, 9 breadth, 15 technical; no thesis. Open: Stanford Engineering Everywhere EE261, EE263, EE364A.
ColumbiaMS: 30 points, at least 15 at 6000 level, elective specializations rather than a fixed core.
Penn (ESE)MSE: 10 course units, 5 core across devices/nano, circuits/computer engineering, information/decision systems.
Cornell (ECE)M.Eng.: 30 credits incl. a two-semester design project.
Princeton (ECE)M.Eng.: eight graded technical courses, four at the 500 level; no thesis.
YaleTerminal MS in Electrical and Computer Engineering.
BrownSc.M. in ECE: eight courses; thesis, non-thesis, or professional tracks.
Dartmouth (Thayer)M.Eng. Electrical/Computer track: core courses in one subfield, electives, a project course.

No matching course found

  • Harvard: no standalone terminal EE master's; SEAS lists an Electrical Engineering PhD, and its S.M. and M.E. pages do not offer a terminal EE M.E.
  • Oxford: no taught EE MSc found; electrical engineering is taught inside the four year undergraduate MEng in Engineering Science, with research degrees (DPhil) at graduate level.
  • MIT is not in the requested list but supplies most open course materials here (OpenCourseWare).

The program, step by step

Module 1

Math and physics readiness (diagnostic plus bootcamp)

about 10 to 12 hours

Goals

  • Solve linear systems and eigenproblems fluently
  • Solve first and second order linear ODEs
  • Work with complex exponentials and phasors
  • Compute expectations and variances

Exercise or deliverable

Write a Python notebook that: solves a 4 by 4 system, finds eigenvalues of a 3 by 3 matrix, solves y'' + 2y' + 5y = 0 analytically and numerically, and plots both.

Assessment

Diagnostic quiz: work the 18.06 Exam 1 and an 18.03 problem set from OCW, timed. Under 70 percent means extend this module.

Module 2

Circuit fundamentals and network analysis

about 10 to 12 hours

Goals

  • Apply KVL and KCL with node and mesh methods
  • Use Thevenin and Norton equivalents and superposition
  • Simulate a circuit in SPICE

Exercise or deliverable

Analyze a 3 node resistive network by hand with node analysis, then verify in ngspice or LTspice and in the Falstad simulator.

Assessment

Graded problem set: 6.002 problem set 1 and 2 (solutions on OCW). Compare your work line by line.

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Module 3

Energy storage, transients, and the Laplace transform

about 10 to 12 hours

Goals

  • Solve RC, RL, and RLC step responses
  • Use Laplace transforms and transfer functions
  • Relate poles to time response

Exercise or deliverable

Build or simulate a series RLC circuit; measure or simulate underdamped, critically damped, and overdamped responses and match them to your pole locations.

Assessment

Write a one page lab report with theory versus measurement plots and an error discussion.

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Module 4

Signals and systems

about 10 to 12 hours

Goals

  • Classify systems (linear, time invariant, causal, stable)
  • Compute convolution in continuous and discrete time
  • Read frequency response

Exercise or deliverable

Implement discrete convolution from scratch in Python, verify against numpy.convolve, and apply it to smooth a noisy recorded signal.

Assessment

Problem set: three convolution problems and one stability proof, written up as a graduate homework.

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Module 5

Fourier analysis and sampling

about 10 to 12 hours

Goals

  • Use Fourier series and transforms and their properties
  • State and apply the sampling theorem
  • Explain aliasing and windowing

Exercise or deliverable

Record or synthesize an audio clip, compute its spectrum with an FFT, downsample with and without an anti-alias filter, and listen to the difference.

Assessment

EE261 problem set (SEE) of your choice, self graded against posted solutions.

Module 6

Linear dynamical systems and feedback control

about 10 to 12 hours

Goals

  • Write state space models
  • Analyze controllability, observability, and stability
  • Design a simple feedback controller

Exercise or deliverable

Model a DC motor in state space, design a state feedback or PID controller in Python, and simulate the step response with a disturbance.

Assessment

Graded: EE263 homework 1 or 2 from SEE; design memo justifying your gains.

Module 7

Semiconductor physics and devices

about 10 to 12 hours

Goals

  • Explain carriers, doping, and drift and diffusion
  • Derive pn junction and MOSFET I-V behavior
  • Connect device physics to circuit models

Exercise or deliverable

Use a nanoHUB MOSFET or pn junction simulator (free account) to sweep doping and plot I-V curves; explain each trend physically.

Assessment

Short exam: five device questions from 6.012 past quizzes on OCW.

Module 8

Analog circuits and amplifiers

about 10 to 12 hours

Goals

  • Bias and analyze single transistor amplifiers
  • Use op amps with feedback and understand their non-ideal specs
  • Read frequency response and stability of amplifiers

Exercise or deliverable

Design a two stage op amp based audio preamplifier with a specified gain and bandwidth; simulate it in SPICE including op amp limitations from a real datasheet.

Assessment

Design review memo: requirements, schematic, simulation, and a comparison table versus spec.

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  • No video this week; the time goes to the exercise.
Module 9

Digital systems and computer architecture

about 10 to 12 hours

Goals

  • Design combinational and sequential logic
  • Write synthesizable HDL
  • Explain a simple CPU datapath and control

Exercise or deliverable

Write a Verilog finite state machine (a traffic light or UART receiver), simulate it on EDA Playground, and synthesize with Yosys.

Assessment

Testbench with at least 10 cases; report pass and fail coverage.

Module 10

Digital signal processing

about 10 to 12 hours

Goals

  • Use the z transform and difference equations
  • Design FIR and IIR filters
  • Implement filters efficiently

Exercise or deliverable

Design a 60 Hz notch filter and a low pass FIR filter, apply both to an ECG style or audio signal, and plot pole zero diagrams and responses.

Assessment

Problem set from 6.341 (OCW) plus your filter design report.

Module 11

Probability, random processes, and communications

about 10 to 12 hours

Goals

  • Model noise as a random process
  • Explain modulation, the matched filter, and error probability
  • Compute bit error rate for a simple scheme

Exercise or deliverable

Simulate BPSK over an additive white Gaussian noise channel in Python, plot BER versus SNR, and compare to theory.

Assessment

Graded: match theory within simulation error; write up assumptions.

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Module 12

Electromagnetics, transmission lines, and RF

about 10 to 12 hours

Goals

  • Use Maxwell's equations in integral and differential form
  • Analyze transmission lines, reflections, and Smith charts
  • Explain antennas and radiation basics

Exercise or deliverable

Compute and plot reflection coefficient and VSWR for a line terminated in several loads; design a quarter wave matching section and check it numerically.

Assessment

Problem set from Ellingson end of chapter exercises (open textbook).

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Module 13

Power systems and power electronics

about 10 to 12 hours

Goals

  • Analyze switching converters in steady state
  • Explain AC power, power factor, and three phase systems
  • Relate machines to power conversion

Exercise or deliverable

Design a 12 V to 5 V, 2 A buck converter on paper using the TI note, then simulate it in LTspice and report ripple and efficiency.

Assessment

Design memo with calculations, simulation evidence, and component stress table.

Module 14

Optimization and the capstone design project

about 20 or more hours

Goals

  • Formulate engineering problems as convex programs
  • Plan, build or simulate, and document a design project like an M.Eng. project

Exercise or deliverable

Capstone: pick one depth area (circuits, signal processing, control, communications, power, or digital). Define a requirement spec, design, simulate or build, test, and write a 10 page report. One part must use optimization (for example optimal filter design or controller tuning with CVXPY).

Assessment

Final review: 15 minute recorded presentation plus report graded on requirements met, analysis quality, testing evidence, and clarity.