The number of degrees of freedom in a system is equal to its number of unknowns minus its number of equations. That is also equal to the number of independent variables in the system. Dependent variables do not contribute degrees of freedom. Ho

Q.E.D. 18: Paxos

Sep 19th, 2016 16m 49s

Leslie Lamport wrote a paper describing the Paxos algorithm in plain English. This is an algorithm that guarantees that a distributed system reaches consensus on the value of an attribute. Lamport claims that the algorithm can be derived from t

QED 17: Pythagoras

Aug 27th, 2016 16m 42s

The Pythagoreans were a cult of Greek mathematicians that believed that all things were composed of large enough integers. Their leader, Pythagoras, is best known for the proof that the square of the hypotenuse of a right triangle is equal to t

QED 16: Elements

Aug 15th, 2016 17m 42s

Euclid's Elements takes a disciplined, formal approach to proving assertions based only on simple axiomatic statements. While most of these axioms are elegant, one of them is more complex and wordy. It seems as if it should be provable from the

QED 15: The Y Combinator

Jul 16th, 2016 19m 42s

The Lambda Calculus uses simple replacement to compute expressions. However, it does not define a way to replace a parameter of a function with the function itself. That would seem to make it impossible to write recursive functions. However, wi

QED 14: Equivocation

Jul 2nd, 2016 16m 32s

Claude Shannon followed up one incredibly important paper with a second of even greater significance. In Communication Theory of Secrecy Systems, he analyzes cryptosystems based on the probabilities of certain plaintext messages given an interc

QED 13: The First Program

Jun 18th, 2016 19m 15s

in a translation of a paper on the Analytical Engine, Ada Lovelace improved upon L. F. Menambrea's work by applying rigor to the calculations that he performed. But then she took things one iteration further. In fact, she took things n iteratio

QED 12: Difference Engine

Jul 20th, 2015 17m 24s

The Difference Engine was a mechanical computer that could calculate tables of numbers based on polynomials. The amazing thing is, though, that it could only add. How then could it accomplish this feat? By the method of differences! Charles Bab

QED 11: The Lambda Calculus

Mar 26th, 2015 17m 18s

Alonzo Church invented The Lambda Calculus as a simple set of rules that, when applied correctly, could compute anything that you could do with a pencil and paper. But all it is is simple replacement. Learn the basics of lambda expressions so t

QED 10: The Two Generals Problem

Mar 9th, 2015 13m 48s

Listener Richard Allen writes to ask about proving enough of a program correct to constrain the number of tests that must be written. I respond that you need both tests and proof. Otherwise, how could you know that the specification is what you

QED 9: The CAP Theorem

Jan 12th, 2015 14m 56s

In 2000, Eric Brewer presented the CAP Conjecture to the Symposium on Principles of Distributed Computing. This states that a distributed system cannot simultaneously guarantee consistency, availability, and partition tolerance. It can, however

Q.E.D. 8: Constructability

Dec 28th, 2014 15m 17s

Knowing that a directed graph is acyclic is useful. If you construct directed graphs in a certain way, then you can prove that they have no cycles. Design systems to produce constructable graphs, and you can take advantage of all of the theorem

QED 7: Topological Ordering

Dec 14th, 2014 15m 14s

In a directed acyclic graph, we can use reachability to determine a partial order. But sometimes we want a total ordering of the nodes to accomplish some result. There are usually many possible total orderings that satisfy the partial ordering.

Partial Order

Dec 3rd, 2014 14m 59s

A fully ordered set is one in which we can tell for any two members which one comes before the other. Think integers. A partially ordered set, however, only gives us an answer for some pairs of nodes. A directed acyclic graph defines a partial

Q.E.D. 5: Fields and Properties

Oct 26th, 2014 16m 27s

The number of degrees of freedom in a solution should match the number in the problem. If you have extra degrees of freedom, then you have to write extra code to keep them in sync. This opens the door for bugs.To count the degrees of freedom

Q. E. D. 4: Factories

Sep 28th, 2014 16m 46s

In the .NET Socket API, if you call methods in the wrong order, the Socket class will throw an exception. Wouldn't it be better if it guided you into the pit of success at compile time? One pattern from the Gang of Four book holds the key to pr

QED 3: First or Default

Sep 16th, 2014 15m 42s

FirstOrDefault is an extension method used in Linq. It is often used incorrectly, leading to exceptions or ignored data. Learn techniques for accessing members of a Linq expression without the possibility of errors."Theorem" and "theory" sound

QED 2: Code Contracts

Sep 8th, 2014 18m 47s

Code Contracts let you express predicates in C# code. This Visual Studio plug in and associated library checks your assertions. It can perform tests at run time, and even prove the predicates at compile time.Leonhard Euler solved the Seven Bri

QED 1: Predicates

Sep 1st, 2014 23m 39s

Apply the principles of predicate calculus to creating reliable software. Use a technique inspired by algebra to confidently change the structure of code without breaking it. And learn how the father of game theory paved the way to the digital

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