Building a training program... for mathematics I want to ask for your advice building my one-year training program for mathematics.
Objectives: 


*

*Keep 'mathematically fit'

*Improve for the pleasure

*Get competent at high-level economics and mathematical/applied statistics. 


Background:


*

*Undergraduate economics

*(Not very mathy) statistics courses which still forced me to self-teach me the basics of linear algebra and probability theory.

*Finished all the Khan Academy quizzes on math. 

*MOOC: Pre-calculus (UC Irvine)

*MOOC: Calculus: Single Variable (U Penn)

*MOOC: Now taking Differential Equations (U Boston) (MATH226.1X, MATH226.2X, MATH226.3X)


Method: An average one hour of deep focus per day without access to courses at (physical) universities nor physicial books (for the first two months). More than one hour is not realistic because of work and hobbies (which both include practicing statistics and data anlysis with R)
Problem: Lack of direction, I spend time+energy drifting around mathy material, pick up a thing or two but not as much as I would if I was focusing deeply at one place at a time. 
Having a clear program would let me do exactly that.
Resources that I have an eye on: 


*

*Statistics 110: Probability (U Harvard)

*Linear Algebra (MIT)

*Introduction to Linear Models and Matrix Algebra (U Harvard)

*Math Camp [for incoming econ graduate students] (Columbia U)
 A: This is a rough sketch of what I think might be good for you. I am also an undergraduate and not in a statistics program, so you should take my opinion with a grain of salt.
Basically, economics and and staistics can be thought of as applications of the mathematical field of analysis. Analysis treats the theory of functions of real or complex variables, as well as metric spaces, measure theory, differential equations and loads of other topics. You could study analysis for your entire life and never learn all of it - there are many open questions.
As for your particular case, I don't know much about economics, but I can say that a good way to learn things related to statistics would be of course to learn the background theory, to which I can recommend a few books that I used in my studies of analysis in undergraduate. I will try to list texts with applications to probability where I can.
For basic analysis (real numbers, complex numbers, sequences, series, continuity, limits, differentiation, integration), the book that I used was Kenneth Ross's book on Elementary Analysis. This is a relatively common text for learning analysis. It doesn't have much application to probability or economics, but it's pretty friendly and introduces everything you need to study analysis further.
For statistics, the chief concern (from my highly limited experience) is integration and probability theory. This is heavily connected to measure theory. For this, a reasonable book with applications to measure theory is Capinski's book "Measure, Integral and Probability." I did not like the exposition in this book because I did not have the probability background. Another standard book without this application that has more analysis in it is the classic book by Folland, which I liked more as a pure mathematician, but again is much more removed from probability theory.
There is another good book with a heavy focus on probability which I am trying to remember but it is escaping me. I will ask a buddy in the class for the title and author and edit this post with more details.
Edit: The book is Probability Essentials by Jacod and Protter. If I remember right, it does contain a few mistakes, but with some prior exposure to measure from either of the other sources, this text is also accessible.
