Recently, I was invited to give a welcome-talk to the new alumni incorporated to the licenciatura of mathematics in the Departament of Maths at CUCEI. Here I write a modified version trying to include some things left in the inkbottle.
The fundamental maths are
- mathematical logic
- set theory
- category theory
which you are learning or going to learn and aimed to give local and global estructure to each theory developed here in math.
But the basic (or pures) are:
- algebra (formal and operational features inter objects, in and inter set of objects, in and inter categories of objects. Estructures: groupoids, semigroups, groups, rings, fields, vector spaces, modules, algebras, Lie groups and Lie algebras,… )
- analysis (math on the limits phenomena, con- and di- vergence, math of measures, optimization, change and direction of change,…)
- geometry (euclidean spaces, abstract-reality, proto-physics, abstract spaces, distance, metric, relativity,..)
- equations (O.D.E., P.D.E., I.E., dynamical systems, chaos, evolution, prediction, simulation,…)
- to what? Response: to make stronger the abstract vision or perception of reality!
- where is topology? Response: among all these four!
- what are they good for? Response: to abstract as many as kinds of math structures or phenomena!
- can be applied? Response: they are endo-applied to themselves, but due that applied maths are source of many could-be-abstracted-maths then it isn’t strange that those applications of basic-maths are greatly appreciated and rewarded!
- may anybody make a living on this knowledge? Response: yes, just look and seek at the right directions: universities, research institutions, science schools, industry, business, goverment,…
- are educative-mathematics, mathematics? Response: no way! there is not a single known theorem. At most conform a body of disorganized psychological statements about mind processes from as many as diverse cultures or countries in the world are.
Of course, those question need a more elaborated answers and only reflect part of my ignorance’s state of affairs. however once enunciated everyone should seek its own internal one, even formulate new.
The elementary maths are those that every-living-one should masters to be well equiped to solve every-day-challenges and business until the first year in a licenciatura, these maths are for any living brain. Even engineers should or could grasp. Those persons who think that learning how to transmit elementary maths they are going to live a intellectual paradise of math gonna find themselves in a struggle with may others which feel themselves mathematicians but far from modern-beautiful-ones, poor little minds! they’re gonna suffer the curse of repeat the most boring part of a teaching career. It is better try to learn good level of math to gain access to better intellectual goals.