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Hi everyone,
I want to get started with Data science and gradually advance to the expert levels. I just do not know where to start. I seek the community's guidance on how can I begin with and advance to expert levels of data science.
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As a start, I suggest learning the following:

\- 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, ...)

\- 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.

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