6.00 Intro: Comp Sci & Programming

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1 6.00 Intro: Comp Sci & Programming SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

2 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

3 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

4 Curriculum Innovation / Unique Aspects / Highlights Majority of non-course-vi students Used 6.00x finger exercises last spring Probably mandatory this spring

5 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

6 6.01 Introduction to Electrical Engineering and Computer Science I SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

7 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

8 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

9 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

10 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

11 6.02: Intro to EECS - II Image Here! SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

12 Bits Signals Packets

13 6.02 Curriculum Prerequisite: 6.01, and or 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

14 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

15 6.02 Outcomes A vertical study of communication across the stack Reliability Sharing (Scalability) à later courses like 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!)

16 6.S02 Intro to EECS II from a Medical Technology Perspective SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

17 6.S02 Curriculum Overview Topics 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. 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

18 6.S02 Structure a typical week Monday Tuesday Wednesday Thursday Friday Lab Lab Lecture Lecture Lab Lab Homework Homework Homework Office Hours 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

19 Highlights/Innovations Hands on Experience with Medical Devices

20 6.041Probabilistic Systems Analysis Image Here! 2009SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

21 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

22 6.041 Structure a typical week MW, 50-min lectures TR, 50-min recitations W, R, or F: 1-hour tutorial Weekly Assignments (about 10% of grade) Two midterms, Final Exam

23 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)

24 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

25 Math for Computer Science Meyer 6.042J/18.062J Leighton Fall students 8 TA s 18 LA s 16 Graders 2 UROPs SP 2010FA 2010SP 2011FA 2011SP 2012FA 2012SP 2013FA 2013SP 2014FA

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 proof- intro.26

27 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

28 A Flipped Classroom 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

29 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

30 6.042 Prereqs High School algebra Single variable calculus Limits Differentiation Integration Series

31 6.042 Outcomes Teamwork & communication Mathematics literacy Math modeling & problem solving Elementary logic & proofs Number theory Graph theory Combinatorics Generating functions Discrete probability

32 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 Topics 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

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