Maths Learning Centre

Our Introduction video is up tommorow. And Monday is our first discussion forum. Topic to be released soon!

"What! you have solved it already?"
"Well, that would be too much to say. I have discovered a suggestive fact, that
is all."

Dr. Watson and Sherlock Holmes
The Sign of Four.

Statistics, the kind of Applied Mathematics which separates men and boys.

The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete at understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms.

Ever had about Russell's Paradox? Let me tell you a little story. Firstly we realize that from set theory that different properties give rise to different sets. Thus if every set was determined by some property, then the whole of set theory would be derivable from the general principles of logic. Now the great German mathematician, philosopher, and one of the founders of modern logic, Gottlob Frege(1848-1925) reasoned, since all of Mathematics is based on set theory, it would follow that the whole of Mathematics is drivable from the general principles of logic. Unfortunately, soon after Frege published his program, the focus British philosopher, mathematician, and antiwar activist Bertrand Russell(1872-1980) found a fatal flaw in Frege's arguments.

Below, we give one of the most popular versions of Russell's Paradox, which is perfectly suited for our purposes.

"By a set, we mean any collection of objects - for example, the set of all even integers or the set of all saxophone players in Brooklyn. The objects that make up a set are called its members or elements. Sets may themselves be members of sets; for example, the set of all sets of integers has sets as its members. Most sets are not members of themselves, the set of cats, for example, is not a member of itself because the set of cats is not a cat. However, there may be sets that do belong to themselves-for example, the set of all sets." Now consider the set of all sets that are not members of themselves. Is that set a member of itself? If it is, it isn't if it isn't it is.

The Brilliance. Let's navigate together some solutions to elementary set theory.

Just because I like Paul Halmos.

The gold prices are surging up and down with different seasonal variations, but my money is sitting in the bank. If only I knew how to read a diagram like this one below, I'd have a certain confidence about the trend levels in markets. What am I talking about? I'm talking about forecasting, and time series a statistical tool which helps my confidence levels.
I'm loading a ton of files on specific problems and solutions in the Math Learning Center group, knock yourself out.

A software developer needs a special kind of ability which distinquishes him and it is not code. A software developer knows mathematical structures. The mathematical structures can be so simple like defining a 1 and 0 as a true or false but they can get complicated bits and megabits. Why don't we start with the elementary discrete Mathematical structures, here? And no one covers this topic explicitly like Kolman& Ross's discrete Mathematica structures

"A geometer like Riemann might almost have foreseen the more important features of the actual world" AS Addington.
Can't wait to discuss open problems like the Riemann hypothesis in the Math Learning Center group, desperately biting my tongue.

Leonhard Euler and the Seven Bridges of Königsberg: Leading To Topology and Graph Theory. In the early 18th century, the citizens of Königsberg spent their days walking on an intricate arrangement of bridges across the waters of the Pregolya River, which surrounded two central land masses connected by a bridge. The first landmass (an island) was connected by four bridges, with two bridges connecting the lower bank, and two bridges connecting the upper bank. The other landmass, which split the Pregel into two branches, was connected to the lower and upper bank by two bridges, with one other bridge connecting both landmasses together. In total, there were seven bridges. According to folklore, a question arose: could a citizen take a walk through the town in such a way that each bridge would be crossed exactly once?
In 1735, Swiss mathematician Leonhard Euler presented a solution to this problem: such a walk was impossible. Let's navigate this walk,