Upload
others
View
16
Download
0
Embed Size (px)
Citation preview
6.00 Intro: Comp Sci & Programming
0
50
100
150
200
250
2009
SP
2010
FA
2010
SP
2011
FA
2011
SP
2012
FA
2012
SP
2013
FA
2013
SP
2014
FA
6.00 Curriculum Overview
� Prereqs: ◦ Elementary Mathematics
� Outcomes: ◦ Basic Programming ◦ Python ◦ Basic tools for data
analysis and simulation ◦ Basic understanding of
probabilities
� Topics ◦ Programming & Python
� Variables, control, functions, scope � Lists � Recursion � Object oriented programming � Exceptions � Debugging
◦ Algorithms � Binary search, Newton � Sorting � Hash tables � Complexity, order of growth
◦ Data analysis � Plotting � Regression, R2 � Monte-Carlo simulation � Clustering (hierarchical, k means) � Lies and statistics
◦ Optimization � Knapsack � Greedy, exhaustive � Graphs,shortest path � Dynamic programming
6.01 Structure – a typical week Monday Tuesday Wednesday Thursday Friday Weekend
Lecture Lecture
Recitation
Pset due
� 2x 1-hour lecture � Grading ◦ Lots of graders
� Recitations: ◦ Tas, 1hr
Curriculum Innovation / Unique Aspects / Highlights � Majority of non-course-VI students � Used 6.00x finger exercises last spring ◦ Probably mandatory this spring
6.00 Outcome
� What can follow-on classes expect from a student who took 6.00
� Requirement for some majors ◦ e.g. bioengineering
� 6.01
0
100
200
300
400
500
600
2009
SP
2010
FA
2010
SP
2011
FA
2011
SP
2012
FA
2012
SP
2013
FA
2013
SP
2014
FA
6.01 Introduction to Electrical Engineering and Computer Science I
6.01 Curriculum Overview
� Prereqs: ◦ Elementary Mathematics
� Outcomes: ◦ EECS Engineering Ethos ◦ Algorithmic Thinking ◦ Modularity and Abstraction ◦ Modeling ◦ Basic Programming ◦ Python ◦ Communication and
Collaboration
� Topics ◦ Basic Programming ◦ Graph Search Algorithms ◦ Signals and Systems ◦ Feedback Control ◦ Resistor Networks ◦ Operational Amplifiers ◦ Equivalent Circuits ◦ Conditional Probability ◦ Probabilistic Inference
6.01 Structure – a typical week Monday Tuesday Wednesday Thursday Friday Weekend
Lecture
Lab Lab
Office Hours
Homework Office Hours Office Hours Homework
� Weekly Assignments: ◦ Online Homeworks (Automatically Graded) ◦ 90-minute “Software” Lab (Individual, Automatically Graded) ◦ 3-hour “Design” Lab (Pairs, Graded by Checkoff with Staff) ◦ 15-minute “Nanoquiz” during Lab (Automatically Graded)
� Two midterms, Final Exam
Curriculum Innovation / Unique Aspects / Highlights
� Hands-on, Project-based Learning ◦ Four substantial projects throughout the semester
� Peer Learning � Undergraduate Involvement ◦ ~40 undergraduate lab assistants every semester ◦ Student Lab Assistant Option
� Software Infrastructure: Help Queue and Tutor
6.01 Outcomes � Exposure to engineering design problems � Understanding of principles of modularity and abstraction � Experience using programming to solve various problems � Experience working in small groups � Exposure to signals and systems; probability and inference;
graph search algorithms; and analog circuits � Increased awareness of the usefulness of math in context
0
50
100
150
200
250
300
2009
SP
2010
FA
2010
SP
2011
FA
2011
SP
2012
FA
2012
SP
2013
FA
2013
SP
2014
FA
6.02: Intro to EECS - II
Image Here!
6.02 Curriculum � Prerequisite: 6.01, and 18.03 or 18.06 � Bits ◦ Source coding – Huffman coding, Lempel-Ziv-Welch compression ◦ Channel coding – Linear block codes, syndrome decoding,
convolutional codes, Viterbi algorithm
� Signals ◦ Noise – probability distributions, optimal detection, SNR ◦ Channels – Physical channels, LTI models for baseband channel,
unit sample response, convolution ◦ Frequency response, filtering ◦ Spectral content of signals via DTFT ◦ Modulation/demodulation, frequency-division multiplexing
� Packets ◦ Statistical multiplexing ◦ Queues – Little’s law, understanding delays ◦ Medium Access Control – TDMA, contention protocols ◦ Routing – Dijkstra’s algorithm, Bellman-Ford distributed algorithm ◦ Reliable transport – retransmissions, sliding windows
Curriculum Innovation / Unique Aspects / Highlights � Bits, Signals, Packets taught as 3 separate but linked modules � 2 lectures, 2 recitations each week; extensive use of Piazza � ~50% grade based on 3 corresponding quizzes � ~50% grade based on 9 problem sets ◦ Theory/conceptual questions ◦ Python-based labs, can be done on student laptops (department labs are just for
TA and LA help, or if students can’t get things to work on their own computers)
� Good course notes at this point, also an OCW version from Fall 2012
� A key sequence of labs: Audiocom where students figure out how to send digital information from the loudspeaker on their laptop to the microphone on their laptop using pulse amplitude modulation of a carrier tone (or multiple tones for FDM!). Good real-world channel, and a real sense of accomplishment in getting this to work. � Exported to HKUST, Stanford, Wisconsin
6.02 Outcomes � A vertical study of communication across the stack ◦ Reliability ◦ Sharing
◦ (Scalability) à later courses like 6.033
� Understanding of widely used algorithms ◦ E.g., Huffman decoding, Viterbi, Dijkstra, sliding window (TCP)
� Design principles, analysis tools, and real-world experimentation w/ Audiocom
� Great background for (or complement to) 6.003, 6.004, 6.011, 6.033, 16.36, …
(Reds currently take advantage of 6.02, but other subjects could too!)
0
10
20
30
40
50
60
70
80
2009
SP
2010
FA
2010
SP
2011
FA
2011
SP
2012
FA
2012
SP
2013
FA
2013
SP
2014
FA
6.S02 Intro to EECS II from a Medical Technology Perspective
6.S02 Curriculum Overview � Prereqs: ◦ Some Programming
Experience � Outcomes: ◦ Analog and Digital Signals ◦ Signals in the Time and
Frequency Domains ◦ Modeling ◦ Basic Programming in
MATLAB ◦ Make Students Aware that
EECS has many Applications in the Medical Sphere.
� Topics ◦ Chemical Signals (Blood
Glucose) � How to measure a physical signal
(noise) � Examining signals in time and
frequency domains � Filtering to improve a measured
signal ◦ Electrocardiography (ECG)
� Physical Basis of Electrocardiography
� ECG analysis in the time and frequency domains
� Clustering and Classification ◦ Magnetic Resonance Imaging
� Signal Model � Image Encoding and
Reconstruction � Clinical Inference
6.S02 Structure – a typical week
� Weekly Assignments: ◦ Prelab (Graded by Checkoff with Staff at the Beginning of Lab) ◦ 3-hour “Design” Lab (Graded by Staff) ◦ Weekly Problem Sets
� Midterm, Final Exam
Monday Tuesday Wednesday Thursday Friday
Lab
Lab
Lab
Lab Lecture Lecture
Homework Homework Homework Office Hours
0 20 40 60 80
100 120 140 160 180
2009
SP
2010
FA
2010
SP
2011
FA
2011
SP
2012
FA
2012
SP
2013
FA
2013
SP
2014
FA
6.041Probabilistic Systems Analysis
Image Here!
!
6.041 Curriculum Overview � Prereqs: ◦ Sets, sequences, limits ◦ Partial derivatives ◦ Double/multiple integrals
� Topics ◦ Probabilistic models ◦ Sample space ◦ Probability ◦ Conditioning and Bayes' rule ◦ Independence ◦ Counting ◦ Random variables ◦ Probability mass and density
functions (PMFs, PDFs) ◦ Expectation and variance ◦ Joint PMFs/PDFs for multiple
random variables ◦ Important distributions
◦ Continuous Bayes' rule ◦ Derived distributions ◦ [Transform techniques] ◦ Covariance and correlation ◦ Iterated expectations ◦ Sum of a random number of random
variables ◦ Weak law of large numbers ◦ Central limit theorem ◦ Bayesian inference (posteriors, MAP,
least squares, linear least squares) ◦ Classical inference (confidence
intervals, linear regression, simple hypotheses testing, significance testing)
◦ Bernoulli process ◦ Poisson process ◦ Markov chains
6.041 Structure – a typical week
� Weekly Assignments (about 10% of grade) � Two midterms, Final Exam
� MW, 50-min lectures � TR, 50-min recitations � W, R, or F: 1-hour tutorial
Curriculum Innovation / Unique Aspects / Highlights
� Also serves general grad. student population
� Interactive problem-solving tutorials � Interactive lectures (Babak, last two terms)
� Solid intro to Bayesian inference � (posteriors, MAP, least squares, linear least squares)
� 6.041x in S2014 ◦ Automatic grading experiment (one assignment, S2013)
6.041 Outcomes � Working knowledge of all the major concepts of basic
probability � Introduction to basic random processes (Poisson, Markov) � Thorough introduction to Bayesian inference � Translate “words” into models � Back and forth between intuition and math � Ready for real-world applications or research
0
50
100
150
200
250
300
2009SP
2010FA
2010SP
2011FA
2011SP
2012FA
2012SP
2013FA
2013SP
2014FA
Math for Computer Science 6.042J/18.062J
Fall13 260 students 8 TA’s 18 LA’s 16 Graders 2 UROPs
Meyer Leighton
proof-‐intro.26
Quick Topic Summary 1. Fundamental Concepts of
Discrete Mathematics (sets, relations, proof methods,… )
2. Discrete Mathematical Structures (numbers, graphs, counting,…)
3. Discrete Probability Theory
A “Flipped” Classroom • Recorded lecture, online feedback
questions, assigned reading before class. • Class sessions with teams of 6-8 students working through graduated problems supervised by LA/TA “coach” • Team writesjoint solution on white board
for coach to assess • Graded for participation
• Don’t care who solves problems as long as everyone understands by end of class. • Heterogeneous teams: men/women,
Freshman/Seniors, Arabs/Jews • Written solutions understandable
by other teams
A “Flipped” Classroom
6.042 Weekly Organization • Three 90 minute class sessions:
§ Online videos & feedback questions before § Reading from text before § “Preparation check” 5 min quiz at start § 3—4 Team Problems supervised by TA/LA
• Problem set • 2 midterms • Final exam
6.042 Prereqs • High School algebra • Single variable calculus • Limits • Differentiation • Integration • Series
6.042 Outcomes – Teamwork & communication – Mathematics literacy – Math modeling & problem solving – Elementary logic & proofs – Number theory – Graph theory – Combinatorics – Generating functions – Discrete probability
6.042 Topics • Contradiction • Proof by cases • Well ordering principle • Propositional logic • Logical quantifiers • Proof rules • Satisfiability • Set & functions • Induction • Invariants • Program correctness • Recursive data • Structural induction • Bijections & cardinality • Uncountable sets • Modular arithmetic
• RSA cryptosystem • Partial orders • Equivalence relations • Walks, paths and cycles • Matrix representation • Graph isomorphism • Bipartite matching • Coloring & connectedness • Trees • Asymptotic notation • Permutations & combinations • Inclusion-exclusion • Generating functions • Probability • Random variables • Sampling & confidence