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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:
  

  
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.

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