first roadmap:

Discrete Mathematics:

1.Discrete Mathematics with Applications by Susanna S. Epp

2.Discrete Mathematics Structures by Koleman, Ross

Proof Writing books:

3.A Transition to Advanced Mathematics by Gary Chartrand

4.An Introduction to Abstract Mathematics by Keane

Pre-Algebra,College Algebra & Pre-Calculus:

5.AGS Pre-Algebra

6.Fearon's Pre-Algebra

7.College Algebra by Jerome E.Kaufmann

8.College Algebra by Blitzer

9.A Graphical Approach to Algebra & Trigonometry by Hornsby, Lial

Calculus:

10.Calculus by Stewart

11.Calculus by Spivak

11.Calculus made easy by Thompson

Differential Equation:

12.A first Course in Differential Equations with modeling applications by Zill

13.Ordinary Differential Equations with Applications Larry C.Andrew

Linear Algebra:

14.Elementary Linear Algebra by Howard Anton

15.Linear Algebra by Friedberg

15.Linear Algebra by SergeLang

15.Linear Algebra by Kenneth Hoffman

Probability and Statistics

16.Mathematical Statistics with Applications Dennis D.Wackerly

17.A First Course in Probability Sheldon Ross

Complex Variables & Complex Analysis:

18.Fundamentals of Complex Analysis with Applications to Engineering and Science by Staff, Snider

19.Complex Variables and Applications by Brown Churchill

Real Analysis:

20.Analysis I&II by Terence Tao

21.Advanced Calculus A Course in Mathematical Analysis by Patrick

22.Principles of Mathematical Analysis by Rudin

23.Elementary Analysis: The Theory of Calculus by Kenneth A.Ross

Abstract Algebra:

24.Abstract Algebra A First Course by Saracino

25.Contemporary Abstract Algebra by Gallian

25.Algebra by Artin

Other Staffs:

26.Introduction to Topology by Gamelin, Greene

27.Applied Combinatorics by Tucker

28.Naive Set Theory by Paul Halmos

29.Introductory Functional Analysis with Applications by Kreyszig

30.Graph Theory Ronald Gould

30.Geometry by Jurgensen Brown

1st interrupt-->

30.Finite-Dimensional Vector Spaces Paul Halmos

30.Schaum's outline of Linear Algebra

30.Linear Algebra and its applications by Gilbert Strang

Advanced:

31.Real Analysis by Royden

32.Real and Complex Analysis by Rudin