# Mathematics - References

## Pure Mathematics Resources

### Algebra

**Linear Algebra:**
1. **"Linear Algebra Done Right" by Sheldon Axler**
   - https://linear.axler.net/
   - Modern approach to linear algebra without determinants first
   - Ideal for proof-based learning

2. **"Linear Algebra" by Hoffman and Kunze**
   - Classic rigorous treatment of linear algebra
   - ISBN: 978-0135367971

3. **MIT OCW Linear Algebra (18.06)**
   - https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/
   - Gilbert Strang's famous course

**Abstract Algebra:**
4. **"Abstract Algebra" by Dummit and Foote**
   - https://www.wiley.com/en-us/Abstract+Algebra%2C+3rd+Edition-p-9780471433347
   - Comprehensive graduate-level text
   - ISBN: 978-0471433347

5. **"Algebra" by Serge Lang**
   - Graduate-level comprehensive reference
   - ISBN: 978-0387953854

6. **"A First Course in Abstract Algebra" by John Fraleigh**
   - Accessible undergraduate introduction
   - ISBN: 978-0201763904

### Analysis

**Real Analysis:**
7. **"Principles of Mathematical Analysis" by Walter Rudin**
   - https://www.mheducation.com/highered/product/principles-mathematical-analysis-rudin/M9780070542358.html
   - Classic "Baby Rudin" for undergraduate analysis
   - ISBN: 978-0070542358

8. **"Real and Complex Analysis" by Walter Rudin**
   - Graduate-level analysis ("Big Rudin")
   - ISBN: 978-0070619876

9. **"Analysis I & II" by Terence Tao**
   - https://terrytao.wordpress.com/books/analysis-i/
   - Rigorous modern treatment
   - ISBN: 978-9811017896

10. **"Understanding Analysis" by Stephen Abbott**
    - Accessible introduction with emphasis on understanding
    - ISBN: 978-1493927111

**Functional Analysis:**
11. **"Functional Analysis" by Walter Rudin**
    - Standard graduate text
    - ISBN: 978-0070619883

12. **"Introductory Functional Analysis with Applications" by Erwin Kreyszig**
    - Applications-oriented approach
    - ISBN: 978-0471504597

**Complex Analysis:**
13. **"Complex Analysis" by Lars Ahlfors**
    - Classic text on complex analysis
    - ISBN: 978-0070006577

14. **"Visual Complex Analysis" by Tristan Needham**
    - Geometric approach to complex analysis
    - ISBN: 978-0198534464

### Topology and Geometry

**General Topology:**
15. **"Topology" by James Munkres**
    - https://www.pearson.com/en-us/subject-catalog/p/topology/P200000003464
    - Standard undergraduate/graduate text
    - ISBN: 978-0134689517

16. **"Introduction to Topological Manifolds" by John Lee**
    - Bridge to differential geometry
    - ISBN: 978-1441979391

**Algebraic Topology:**
17. **"Algebraic Topology" by Allen Hatcher**
    - https://pi.math.cornell.edu/~hatcher/AT/ATpage.html
    - Free online, comprehensive treatment

18. **"A Concise Course in Algebraic Topology" by J.P. May**
    - https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
    - Free online, graduate level

**Differential Geometry:**
19. **"Introduction to Smooth Manifolds" by John Lee**
    - Modern comprehensive treatment
    - ISBN: 978-1441999818

20. **"Riemannian Geometry" by Manfredo do Carmo**
    - Classic text on Riemannian geometry
    - ISBN: 978-0817634902

### Number Theory

21. **"An Introduction to the Theory of Numbers" by Hardy and Wright**
    - Classic comprehensive text
    - ISBN: 978-0199219865

22. **"A Classical Introduction to Modern Number Theory" by Ireland and Rosen**
    - Bridge to algebraic number theory
    - ISBN: 978-1441930941

23. **"Algebraic Number Theory" by Neukirch**
    - Standard graduate reference
    - ISBN: 978-3540653998

24. **"Prime Numbers and the Riemann Hypothesis" by Mazur and Stein**
    - https://wstein.org/rh/
    - Accessible introduction to analytic number theory

### Logic and Foundations

25. **"Set Theory" by Kenneth Kunen**
    - Standard graduate text
    - ISBN: 978-1848900509

26. **"Introduction to Mathematical Logic" by Mendelson**
    - Comprehensive logic text
    - ISBN: 978-1482237726

27. **"Proofs and Types" by Girard, Lafont, and Taylor**
    - http://www.paultaylor.eu/stable/Proofs+Types.html
    - Free online, proof theory and type theory

## Applied Mathematics Resources

### Differential Equations

**Ordinary Differential Equations:**
28. **"Ordinary Differential Equations" by Tenenbaum and Pollard**
    - Comprehensive problem-solving approach
    - ISBN: 978-0486649405

29. **"Nonlinear Dynamics and Chaos" by Steven Strogatz**
    - https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos
    - Accessible introduction to dynamical systems
    - ISBN: 978-0813349107

30. **"Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Hirsch, Smale, and Devaney**
    - Modern treatment with linear algebra perspective
    - ISBN: 978-0123820105

**Partial Differential Equations:**
31. **"Partial Differential Equations" by Lawrence C. Evans**
    - Standard graduate text
    - ISBN: 978-0821849743

32. **"Applied Partial Differential Equations" by Haberman**
    - Engineering-oriented approach
    - ISBN: 978-0134995434

33. **"Introduction to Partial Differential Equations" by Strauss**
    - Accessible undergraduate text
    - ISBN: 978-0470054567

### Numerical Analysis

34. **"Numerical Analysis" by Burden and Faires**
    - https://www.cengage.com/c/numerical-analysis-10e-burden/
    - Comprehensive undergraduate text
    - ISBN: 978-1305253667

35. **"Numerical Linear Algebra" by Trefethen and Bau**
    - https://people.maths.ox.ac.uk/trefethen/text.html
    - Standard text for numerical linear algebra
    - ISBN: 978-0898713619

36. **"Matrix Computations" by Golub and Van Loan**
    - Comprehensive reference for matrix algorithms
    - ISBN: 978-1421407944

37. **"Approximation Theory and Approximation Practice" by Trefethen**
    - Modern treatment with Chebfun examples
    - ISBN: 978-1611972399

38. **"Finite Difference Methods for Ordinary and Partial Differential Equations" by LeVeque**
    - Comprehensive numerical PDEs text
    - ISBN: 978-0898716290

39. **"The Finite Element Method" by Hughes**
    - Engineering-oriented FEM text
    - ISBN: 978-0486411811

### Optimization

40. **"Convex Optimization" by Boyd and Vandenberghe**
    - https://web.stanford.edu/~boyd/cvxbook/
    - Free online, standard reference
    - ISBN: 978-0521833783

41. **"Numerical Optimization" by Nocedal and Wright**
    - Comprehensive algorithms text
    - ISBN: 978-0387303031

42. **"Introduction to Linear Optimization" by Bertsimas and Tsitsiklis**
    - Modern LP and integer programming
    - ISBN: 978-1886529199

43. **"Nonlinear Programming" by Bazaraa, Sherali, and Shetty**
    - Comprehensive nonlinear optimization
    - ISBN: 978-0471486008

44. **"Integer Programming" by Conforti, Cornuejols, and Zambelli**
    - Modern IP text
    - ISBN: 978-3319110073

### Mathematical Modeling

45. **"Mathematical Modeling" by Meerschaert**
    - Comprehensive modeling text
    - ISBN: 978-0123869128

46. **"A First Course in Mathematical Modeling" by Giordano, Fox, and Horton**
    - Accessible introduction
    - ISBN: 978-1285050904

47. **"Mathematical Models in Biology" by Edelstein-Keshet**
    - https://www.siam.org/publications/books/classics-in-applied-mathematics/cl46
    - SIAM Classics, biological modeling
    - ISBN: 978-0898715545

48. **"Scaling" by Barenblatt**
    - Dimensional analysis and similarity
    - ISBN: 978-0521533942

## Statistics and Probability Resources

### Probability Theory

49. **"A First Course in Probability" by Sheldon Ross**
    - Standard undergraduate text
    - ISBN: 978-0134753119

50. **"Probability and Random Processes" by Grimmett and Stirzaker**
    - Rigorous undergraduate/graduate text
    - ISBN: 978-0198572220

51. **"Probability: Theory and Examples" by Rick Durrett**
    - https://services.math.duke.edu/~rtd/PTE/pte.html
    - Free online, graduate text
    - ISBN: 978-1108473682

52. **"Stochastic Processes" by Sheldon Ross**
    - Standard stochastic processes text
    - ISBN: 978-0471120629

53. **"Brownian Motion and Stochastic Calculus" by Karatzas and Shreve**
    - Graduate-level stochastic calculus
    - ISBN: 978-0387976556

### Statistical Inference

54. **"Statistical Inference" by Casella and Berger**
    - Standard graduate inference text
    - ISBN: 978-0534243128

55. **"All of Statistics" by Larry Wasserman**
    - https://www.stat.cmu.edu/~larry/all-of-statistics/
    - Concise comprehensive treatment
    - ISBN: 978-0387402727

56. **"Mathematical Statistics and Data Analysis" by John Rice**
    - Accessible comprehensive text
    - ISBN: 978-0534399429

57. **"Theory of Point Estimation" by Lehmann and Casella**
    - Graduate estimation theory
    - ISBN: 978-0387985022

58. **"Testing Statistical Hypotheses" by Lehmann and Romano**
    - Graduate hypothesis testing theory
    - ISBN: 978-0387988641

### Bayesian Statistics

59. **"Bayesian Data Analysis" by Gelman et al.**
    - http://www.stat.columbia.edu/~gelman/book/
    - Standard Bayesian reference
    - ISBN: 978-1439840955

60. **"A First Course in Bayesian Statistical Methods" by Hoff**
    - Accessible introduction
    - ISBN: 978-0387922997

61. **"Bayesian Theory" by Bernardo and Smith**
    - Theoretical Bayesian foundations
    - ISBN: 978-0471494645

### Statistical Learning

62. **"The Elements of Statistical Learning" by Hastie, Tibshirani, and Friedman**
    - https://hastie.su.domains/ElemStatLearn/
    - Free online, comprehensive ML/statistics
    - ISBN: 978-0387848570

63. **"An Introduction to Statistical Learning" by James et al.**
    - https://www.statlearning.com/
    - Free online, accessible introduction
    - ISBN: 978-1071614174

64. **"Pattern Recognition and Machine Learning" by Bishop**
    - https://www.microsoft.com/en-us/research/people/cmbishop/prml-book/
    - Comprehensive probabilistic ML
    - ISBN: 978-0387310732

65. **"Machine Learning: A Probabilistic Perspective" by Kevin Murphy**
    - https://probml.github.io/pml-book/
    - Comprehensive modern treatment
    - ISBN: 978-0262018029

### Time Series

66. **"Time Series Analysis" by Box, Jenkins, and Reinsel**
    - Classic ARIMA methodology
    - ISBN: 978-1118675021

67. **"Forecasting: Principles and Practice" by Hyndman and Athanasopoulos**
    - https://otexts.com/fpp3/
    - Free online, practical forecasting
    - ISBN: 978-0987507112

68. **"Time Series Analysis and Its Applications" by Shumway and Stoffer**
    - https://www.stat.pitt.edu/stoffer/tsa4/
    - Comprehensive with R examples
    - ISBN: 978-3319524511

## Computational Mathematics Software

### Computer Algebra Systems

69. **Mathematica/Wolfram Language**
    - https://www.wolfram.com/mathematica/
    - Comprehensive symbolic computation

70. **Maple**
    - https://www.maplesoft.com/products/maple/
    - Symbolic and numeric computation

71. **SageMath**
    - https://www.sagemath.org/
    - Free open-source mathematics software
    - Python-based, comprehensive

72. **SymPy**
    - https://www.sympy.org/
    - Python symbolic mathematics library
    - Open-source

73. **Maxima**
    - https://maxima.sourceforge.io/
    - Free computer algebra system
    - Descendant of DOE Macsyma

### Numerical Computing

74. **MATLAB**
    - https://www.mathworks.com/products/matlab.html
    - Industry-standard numerical computing

75. **GNU Octave**
    - https://octave.org/
    - Free MATLAB-compatible environment

76. **Julia**
    - https://julialang.org/
    - High-performance scientific computing
    - Open-source

77. **NumPy**
    - https://numpy.org/
    - Python numerical computing foundation

78. **SciPy**
    - https://scipy.org/
    - Python scientific computing library

79. **LAPACK**
    - https://www.netlib.org/lapack/
    - Linear algebra package

80. **BLAS**
    - https://www.netlib.org/blas/
    - Basic Linear Algebra Subprograms

### Optimization Software

81. **CPLEX (IBM)**
    - https://www.ibm.com/analytics/cplex-optimizer
    - Commercial LP/MIP solver

82. **Gurobi**
    - https://www.gurobi.com/
    - Commercial optimization solver

83. **MOSEK**
    - https://www.mosek.com/
    - Conic optimization solver

84. **CVXPY**
    - https://www.cvxpy.org/
    - Python convex optimization

85. **OR-Tools (Google)**
    - https://developers.google.com/optimization
    - Open-source optimization tools

86. **AMPL**
    - https://ampl.com/
    - Algebraic modeling language

87. **PuLP**
    - https://coin-or.github.io/pulp/
    - Python LP/MIP modeling

88. **JuMP**
    - https://jump.dev/
    - Julia mathematical optimization

### Statistical Software

89. **R**
    - https://www.r-project.org/
    - Statistical computing and graphics

90. **RStudio**
    - https://www.rstudio.com/
    - IDE for R

91. **Python (statsmodels)**
    - https://www.statsmodels.org/
    - Statistical modeling in Python

92. **Stan**
    - https://mc-stan.org/
    - Bayesian inference platform

93. **PyMC**
    - https://www.pymc.io/
    - Probabilistic programming in Python

94. **SAS**
    - https://www.sas.com/
    - Enterprise analytics platform

95. **Stata**
    - https://www.stata.com/
    - Statistical analysis software

96. **SPSS**
    - https://www.ibm.com/products/spss-statistics
    - Statistical analysis software

### Proof Assistants and Formal Verification

97. **Lean**
    - https://leanprover.github.io/
    - Interactive theorem prover
    - Mathlib library

98. **Coq**
    - https://coq.inria.fr/
    - Proof assistant and programming language

99. **Isabelle**
    - https://isabelle.in.tum.de/
    - Generic proof assistant

100. **Agda**
     - https://wiki.portal.chalmers.se/agda/
     - Dependently typed programming language

101. **Metamath**
     - http://us.metamath.org/
     - Formal proof database

102. **HOL Light**
     - https://www.cl.cam.ac.uk/~jrh13/hol-light/
     - Interactive theorem prover

### Visualization

103. **Matplotlib**
     - https://matplotlib.org/
     - Python 2D plotting

104. **GeoGebra**
     - https://www.geogebra.org/
     - Dynamic mathematics software

105. **Desmos**
     - https://www.desmos.com/
     - Online graphing calculator

106. **Manim**
     - https://www.manim.community/
     - Mathematical animation engine

107. **TikZ/PGF**
     - https://github.com/pgf-tikz/pgf
     - LaTeX graphics

108. **Asymptote**
     - https://asymptote.sourceforge.io/
     - Vector graphics language

### LaTeX and Typesetting

109. **LaTeX**
     - https://www.latex-project.org/
     - Document preparation system

110. **Overleaf**
     - https://www.overleaf.com/
     - Online LaTeX editor

111. **MathJax**
     - https://www.mathjax.org/
     - Web mathematics display

112. **KaTeX**
     - https://katex.org/
     - Fast math typesetting for web

113. **TeXstudio**
     - https://www.texstudio.org/
     - LaTeX IDE

## Online Resources and Databases

### Mathematical Archives

114. **arXiv Mathematics**
     - https://arxiv.org/archive/math
     - Preprint server for mathematics

115. **MathSciNet**
     - https://mathscinet.ams.org/
     - AMS mathematical reviews database

116. **zbMATH**
     - https://zbmath.org/
     - Mathematics abstract service

117. **OEIS (Online Encyclopedia of Integer Sequences)**
     - https://oeis.org/
     - Integer sequence database

### Digital Libraries

118. **Project Euclid**
     - https://projecteuclid.org/
     - Mathematics and statistics publications

119. **JSTOR**
     - https://www.jstor.org/
     - Academic journal archive

120. **Mathematical Association of America**
     - https://www.maa.org/
     - Publications and resources

121. **American Mathematical Society**
     - https://www.ams.org/
     - Publications, conferences, and resources

122. **SIAM (Society for Industrial and Applied Mathematics)**
     - https://www.siam.org/
     - Applied mathematics resources

### Open Educational Resources

123. **MIT OpenCourseWare - Mathematics**
     - https://ocw.mit.edu/courses/mathematics/
     - Free course materials

124. **Khan Academy**
     - https://www.khanacademy.org/math
     - Free online math education

125. **Brilliant**
     - https://brilliant.org/
     - Interactive math and science courses

126. **3Blue1Brown**
     - https://www.3blue1brown.com/
     - Visual mathematics explanations
     - YouTube: https://www.youtube.com/c/3blue1brown

127. **Paul's Online Math Notes**
     - https://tutorial.math.lamar.edu/
     - Free calculus and differential equations notes

128. **Mathigon**
     - https://mathigon.org/
     - Interactive mathematics courses

### Problem Databases

129. **Art of Problem Solving**
     - https://artofproblemsolving.com/
     - Competition mathematics resources

130. **Project Euler**
     - https://projecteuler.net/
     - Computational mathematics problems

131. **Putnam Archive**
     - https://kskedlaya.org/putnam-archive/
     - Putnam Competition problems

132. **IMO (International Mathematical Olympiad)**
     - https://www.imo-official.org/
     - International olympiad problems

## Journals and Publications

### Pure Mathematics

133. **Annals of Mathematics**
     - https://annals.math.princeton.edu/
     - Premier general mathematics journal

134. **Inventiones Mathematicae**
     - https://www.springer.com/journal/222
     - Leading research journal

135. **Journal of the American Mathematical Society**
     - https://www.ams.org/journals/jams/
     - AMS flagship journal

136. **Acta Mathematica**
     - https://www.springer.com/journal/11511
     - Prestigious general mathematics

137. **Duke Mathematical Journal**
     - https://www.dukeupress.edu/Duke-Mathematical-Journal
     - Leading research journal

### Applied Mathematics

138. **SIAM Review**
     - https://www.siam.org/publications/journals/siam-review-sirev
     - Expository applied mathematics

139. **SIAM Journal on Applied Mathematics**
     - https://www.siam.org/publications/journals/siam-journal-on-applied-mathematics-siap
     - Applied mathematics research

140. **SIAM Journal on Numerical Analysis**
     - https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum
     - Numerical analysis research

141. **Journal of Computational Physics**
     - https://www.journals.elsevier.com/journal-of-computational-physics
     - Computational methods

142. **Communications on Pure and Applied Mathematics**
     - https://onlinelibrary.wiley.com/journal/10970312
     - Analysis and applied mathematics

### Statistics

143. **Annals of Statistics**
     - https://imstat.org/journals-and-publications/annals-of-statistics/
     - Premier statistics journal

144. **Journal of the American Statistical Association**
     - https://www.tandfonline.com/journals/uasa20
     - Leading statistics journal

145. **Journal of the Royal Statistical Society**
     - https://rss.org.uk/news-publication/publications/journals/
     - Series A, B, and C

146. **Biometrika**
     - https://academic.oup.com/biomet
     - Statistical methodology

147. **Statistical Science**
     - https://imstat.org/journals-and-publications/statistical-science/
     - Review and discussion

### Probability

148. **Annals of Probability**
     - https://imstat.org/journals-and-publications/annals-of-probability/
     - Premier probability journal

149. **Probability Theory and Related Fields**
     - https://www.springer.com/journal/440
     - Leading probability research

150. **Stochastic Processes and their Applications**
     - https://www.journals.elsevier.com/stochastic-processes-and-their-applications
     - Applied probability

### Optimization

151. **Mathematical Programming**
     - https://www.springer.com/journal/10107
     - Flagship optimization journal

152. **SIAM Journal on Optimization**
     - https://www.siam.org/publications/journals/siam-journal-on-optimization-siopt
     - Optimization research

153. **Operations Research**
     - https://pubsonline.informs.org/journal/opre
     - INFORMS flagship journal

154. **Journal of Optimization Theory and Applications**
     - https://www.springer.com/journal/10957
     - Optimization theory

## Conferences and Organizations

### Major Conferences

155. **International Congress of Mathematicians (ICM)**
     - https://www.mathunion.org/icm/
     - Quadrennial world mathematics congress

156. **Joint Mathematics Meetings (JMM)**
     - https://www.jointmathematicsmeetings.org/
     - AMS/MAA annual meeting

157. **SIAM Annual Meeting**
     - https://www.siam.org/conferences-events
     - Applied mathematics conference

158. **International Symposium on Mathematical Programming (ISMP)**
     - https://www.mathopt.org/
     - Triennial optimization conference

159. **Joint Statistical Meetings (JSM)**
     - https://www.amstat.org/meetings/joint-statistical-meetings
     - Largest statistics conference

160. **International Conference on Machine Learning (ICML)**
     - https://icml.cc/
     - Machine learning research

161. **NeurIPS**
     - https://nips.cc/
     - Machine learning and computational neuroscience

### Professional Organizations

162. **American Mathematical Society (AMS)**
     - https://www.ams.org/

163. **Mathematical Association of America (MAA)**
     - https://www.maa.org/

164. **Society for Industrial and Applied Mathematics (SIAM)**
     - https://www.siam.org/

165. **American Statistical Association (ASA)**
     - https://www.amstat.org/

166. **Institute of Mathematical Statistics (IMS)**
     - https://imstat.org/

167. **Mathematical Optimization Society (MOS)**
     - https://www.mathopt.org/

168. **International Mathematical Union (IMU)**
     - https://www.mathunion.org/

169. **European Mathematical Society (EMS)**
     - https://euromathsoc.org/

170. **London Mathematical Society (LMS)**
     - https://www.lms.ac.uk/

## Online Courses and MOOCs

### Foundational Courses

171. **Calculus (MIT 18.01, 18.02)**
     - https://ocw.mit.edu/courses/mathematics/
     - Single and multivariable calculus

172. **Linear Algebra (MIT 18.06)**
     - https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/
     - Gilbert Strang's course

173. **Real Analysis (MIT 18.100)**
     - https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
     - Rigorous analysis

174. **Abstract Algebra (Harvard Math 122)**
     - https://www.extension.harvard.edu/course-catalog/courses/abstract-algebra
     - Group theory and beyond

### Applied and Computational

175. **Differential Equations (MIT 18.03)**
     - https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/
     - ODEs course

176. **Numerical Methods (MIT 18.330)**
     - https://github.com/mitmath/18330
     - Julia-based numerical methods

177. **Convex Optimization (Stanford)**
     - https://www.edx.org/learn/engineering/stanford-university-convex-optimization
     - Boyd's course on edX

178. **Machine Learning (Stanford CS229)**
     - http://cs229.stanford.edu/
     - Andrew Ng's course

### Statistics and Data Science

179. **Statistics 110: Probability (Harvard)**
     - https://projects.iq.harvard.edu/stat110
     - Joe Blitzstein's course

180. **Statistical Learning (Stanford)**
     - https://www.edx.org/learn/statistics/stanford-university-statistical-learning
     - Hastie and Tibshirani

181. **Data Science Specialization (Johns Hopkins)**
     - https://www.coursera.org/specializations/jhu-data-science
     - R-based data science

182. **Bayesian Statistics (Duke)**
     - https://www.coursera.org/specializations/bayesian-statistics
     - Bayesian methods

## Community Resources

### Forums and Q&A

183. **Mathematics Stack Exchange**
     - https://math.stackexchange.com/
     - Q&A for mathematics

184. **MathOverflow**
     - https://mathoverflow.net/
     - Research-level Q&A

185. **Cross Validated**
     - https://stats.stackexchange.com/
     - Statistics Q&A

186. **Computational Science Stack Exchange**
     - https://scicomp.stackexchange.com/
     - Scientific computing Q&A

187. **Operations Research Stack Exchange**
     - https://or.stackexchange.com/
     - OR and optimization Q&A

### Blogs and Expository Sites

188. **Terence Tao's Blog**
     - https://terrytao.wordpress.com/
     - Fields Medalist's research blog

189. **Gowers's Weblog**
     - https://gowers.wordpress.com/
     - Timothy Gowers's mathematical blog

190. **The n-Category Cafe**
     - https://golem.ph.utexas.edu/category/
     - Category theory and related areas

191. **Quanta Magazine - Mathematics**
     - https://www.quantamagazine.org/mathematics/
     - Accessible mathematics journalism

192. **American Mathematical Monthly**
     - https://www.tandfonline.com/toc/uamm20/current
     - Expository mathematics

193. **What's New (Terence Tao)**
     - https://terrytao.wordpress.com/
     - Research updates and exposition

### Mathematical Software Communities

194. **Julia Discourse**
     - https://discourse.julialang.org/
     - Julia programming community

195. **R-help and R-devel**
     - https://www.r-project.org/mail.html
     - R mailing lists

196. **SciPy Mailing Lists**
     - https://scipy.org/community/
     - Scientific Python community

197. **Lean Zulip Chat**
     - https://leanprover.zulipchat.com/
     - Lean theorem prover community

198. **CVXPY Community**
     - https://github.com/cvxpy/cvxpy/discussions
     - Convex optimization community

## Specialized Topics

### Financial Mathematics

199. **"Options, Futures, and Other Derivatives" by Hull**
     - Standard derivatives text
     - ISBN: 978-0134472089

200. **"Stochastic Calculus for Finance" by Shreve**
     - Two-volume rigorous treatment
     - ISBN: 978-0387249681

201. **QuantLib**
     - https://www.quantlib.org/
     - Open-source quantitative finance library

### Cryptography

202. **"An Introduction to Mathematical Cryptography" by Hoffstein, Pipher, and Silverman**
     - Mathematical foundations
     - ISBN: 978-1493917105

203. **"A Course in Computational Algebraic Number Theory" by Cohen**
     - Algorithmic number theory
     - ISBN: 978-3540556404

### Mathematical Biology

204. **"Mathematical Biology" by Murray**
     - Two-volume standard reference
     - ISBN: 978-0387952239

205. **"Modeling Differential Equations in Biology" by Clifford Henry Taubes**
     - Accessible introduction
     - ISBN: 978-0130173256

### Information Theory

206. **"Elements of Information Theory" by Cover and Thomas**
     - Standard information theory text
     - ISBN: 978-0471241959

207. **"Information Theory, Inference and Learning Algorithms" by MacKay**
     - http://www.inference.org.uk/mackay/itila/
     - Free online

### Category Theory

208. **"Categories for the Working Mathematician" by Mac Lane**
     - Standard category theory text
     - ISBN: 978-0387984032

209. **"Category Theory in Context" by Emily Riehl**
     - http://www.math.jhu.edu/~eriehl/context.pdf
     - Free online modern treatment

210. **nLab**
     - https://ncatlab.org/
     - Mathematics wiki with category theory focus

## Total Reference Count: 210+

This document provides comprehensive references including:
- 30+ pure mathematics textbooks and resources
- 25+ applied mathematics and numerical analysis references
- 30+ statistics and probability resources
- 40+ software tools and packages
- 20+ journals and publications
- 15+ conferences and organizations
- 20+ online courses and MOOCs
- 15+ community resources and forums
- 15+ specialized topic references

**Key Resource Summary:**
- **Pure Math Textbooks:** Rudin, Munkres, Dummit-Foote, Hatcher
- **Applied Math Textbooks:** Strogatz, Evans, Boyd-Vandenberghe, Trefethen
- **Statistics Textbooks:** Casella-Berger, Gelman, Hastie-Tibshirani-Friedman
- **Software:** MATLAB, Julia, R, Python (NumPy/SciPy), SageMath, Mathematica
- **Optimization:** CPLEX, Gurobi, CVXPY, JuMP
- **Proof Assistants:** Lean, Coq, Isabelle
- **Organizations:** AMS, MAA, SIAM, ASA, IMS
- **Online Learning:** MIT OCW, Coursera, edX, Khan Academy
