As a start, I suggest learning the following:

Statistics:

\- probability (distributions, basic manipulations)

\- statistical summaries (univariate and bivariate)

\- hypothesis testing / confidence intervals

\- linear regression

Linear Algebra:

\- basic understanding of arranging data in vectors and matrices

\- operators (matrix multiplication, ...)

Calculus:

\- limits

\- basic differentiation and integration (at least of polynomials)

Information Theory (Discrete):

\- entropy, joint entropy, conditional entropy, mutual information

For statistics, I highly recommend:

"Practice of Business Statistics"

by David S. Moore, George P. McCabe, William M. Duckworth and Stanley L. Sclove

ISBN-13: 978-0716757238

To learn about machine learning, I recommend both of these:

"Computer Systems That Learn"

by Weiss and Kulikowski

ISBN-13: 978-1558600652

"Data Mining: Practical Machine Learning Tools and Techniques"

by Ian H. Witten, Eibe Frank, Mark A. Hall and Christopher J. Pal

The 4th edition (2016) has ISBN-13: 978-0128042915, though older editions are fine and likely less expensive.