Proof portfolio
Write ten complete proofs in LaTeX: induction, contradiction, combinatorics, graphs.
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Computer science · 16Intermediate
Theoretical Computer Scientist
Future computer science master's students.
Proofs, combinatorics, logic and graphs, then Stanford algorithms and advanced data structures up to quantum algorithms.
463hours of coursework
47weeks at 10 h
4steps
19courses
4universities
Target skills
AlgorithmsGraph TheoryMathematical ModelingTheoretical Computer ScienceArithmeticProgramming PrinciplesCryptographyDeductive ReasoningProbabilityStatisticsEncryptionPython Programming
Skill labels as listed on Coursera.
Target jobs
- Computer science PhD student
- Algorithms engineer
- Researcher
Progression
- 1University of California San DiegoBeginnerPython
Stated prerequisites: Basic math (fractions, squares), basic Python (functions, loops, recursion)
Show the 5 courses
Course Level Length Rating (reviews) Mathematical Thinking in Computer Science Beginner 42 h 4.4 (2,289) Combinatorics and Probability Beginner 23 h 4.6 (874) Introduction to Graph Theory Beginner 21 h 4.5 (1,073) Number Theory and Cryptography Beginner 17 h 4.5 (610) Delivery Problem Beginner 13 h 4.7 (376) - 2University of London (Goldsmiths)Beginner
Show the 5 courses
Course Level Length Rating (reviews) Mathematical Foundations for Computing Beginner 20 h — Applied Mathematical Methods for Computing Beginner 19 h — Geometry and Calculus for Computing Beginner 15 h — Logic and Reasoning for Computing Intermediate 18 h — Algorithms and Complexity Intermediate 19 h — - 3Stanford University (Stanford Online)IntermediateC, Java, Python
Stated prerequisites: Programming in at least one language (C, Java or Python); familiarity with proofs (induction, contradiction); discrete probability
Show the 4 courses
Course Level Length Rating (reviews) Divide and Conquer, Sorting and Searching, and Randomized Algorithms Intermediate 15 h 4.8 (5,342) Graph Search, Shortest Paths, and Data Structures Intermediate 14 h 4.8 (2,002) Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming Intermediate 15 h 4.8 (1,279) Shortest Paths Revisited, NP-Complete Problems and What To Do About Them Intermediate 13 h 4.8 (832) - 4University of Colorado BoulderAdvancedPythonacademic credit
Stated prerequisites: Some background in calculus, probability theory and Python programming
Show the 5 courses
Course Level Length Rating (reviews) Algorithms for Searching, Sorting, and Indexing Intermediate 36 h 4.7 (544) Trees and Graphs: Basics Advanced 34 h 4.6 (194) Dynamic Programming, Greedy Algorithms Advanced 38 h 4.7 (282) Approximation Algorithms and Linear Programming Advanced 46 h 4.8 (67) Advanced Data Structures, RSA and Quantum Algorithms Advanced 45 h 4.6 (70)
With Coursera Plus
This path takes 463 hours, about 11 months at 10 hours a week. A Coursera Plus subscription gives access to most of its courses during that time.
Projects to build
Graph library
Implement Dijkstra, Kruskal and breadth-first search, then compare their run times on real networks.
NP-hard problem
Compare an exact solution and three travelling salesman heuristics on growing instances.
Free textbooks
Mathematics for Computer ScienceE. Lehman, F. T. Leighton, A. R. Meyer (MIT)Free, CC BY-SA
AlgorithmsJeff EricksonFree, CC BY 4.0
Open Data StructuresPat MorinFree, CC BY 2.5