An Introduction to Complex Systems

Paul Fieguth


Textbook Further Reading Page (see also Reading Questions page)

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Chapter 1: Introduction
References:

1. C. Martenson. The Crash Course: The Unsustainable Future of our Economy, Energy, and Environment. Wiley, 2011.
2. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
3. A. Weisman. The World Without Us. Picador, 2007.
4. R. Wright. A Short History of Progress. House of Anansi Press, 2004.

Chapter 2: Global Warming
Further Reading Links:

Global Warming, Climate Change

References:

1. K. Emanual. What We Know About Climate Change. MIT Press, 2012.
2. A. Johnson and N. White. Ocean acidification: The other climate change issue. American Scientist, 102(1), 2014.
3. L. Kump et al. The Earth System. Prentice Hall, 2010.
4. F. Mackenzie. Our Changing Planet. Prentice Hall, 2011.
5. B. McKibben. The Global Warming Reader. OR Books, 2011.
6. R. Primack. Walden Warming. University of Chicago Press, 2014.
7. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.

Chapter 3: Systems Theory
Further Reading Links:

Systems theory: System, Systems theory, Systems of Systems, Steady state

Thermodynamics: Thermodynamics, Entropy, Energy, Landauer’s principle

Global Flows: Water cycle, Nitrogen cycle, Carbon cycle, Earth’s Energy Budget,
Vitousek et al. Human Alteration of the Global Nitrogen Cycle, Issues in Ecology, 1997.

Examples: EROEI, Environmental economics, Full-cost accounting, Environmental accounting, Externalities, Maximum power principle, Technological Singularity

References:

1. Special issue on the singularity. IEEE Spectrum 45(6), 2008.
2. J. Diamond. Collapse: How Societies Choose to Fail or Succeed. Penguin, 2011.
3. A. Ghosh. Dynamic Systems for Everyone: Understanding How Our World Works. Springer, 2015.
4. J. Greer. How Civilizations Fall: A Theory of Catabolic Collapse. Unpublished, 2005.
5. R. Heinberg. Searching for a Miracle: Net Energy Limits & the Fate of Industrial Society. Post Carbon Institute, 2009.
6. C. Hidalgo. Why Information Grows: The Evolution of Order, from Atoms to Economies. Basic Books, 2015.
7. T. Homer-Dixon. The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization. Knopf, 2006.
8. D. Meadows. Thinking in Systems: A Primer. Chelsea Green, 2008.
9. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
10. H. Odum. Environmental Accounting: Emergy and Environmental Decision Making. Wiley, 1996.
11. H. Odum. Environment, Power, and Society for the Twenty-First Century. Columbia, 2007.
12. J. Salatin. Salad Bar Beef. Polyface, 1996.
13. S. Schaltegger and R. Burritt. Contemporary Environmental Accounting: Issues, Concepts and Practice. Greenleaf Publishing, 2000.
14. E. Schumacher. Small is Beautiful: A Study of Economics as if People Mattered. Vintage Digital, 2011.
15. J. Smillie and G. Gershuny. The Soul of Soil. Chelsea Green, 1999.
16. K. Stowe. An Introduction to Thermodynamics and Statistical Mechanics. Cambridge, 2007.
17. J. Tainter. The Collapse of Complex Societies. Cambridge, 1990.
18. M. Wackernagel and W. Rees. Our Ecological Footprint. New Society, 1995.
19. J. Weaver. Root Development of Field Crops. McGraw Hill, 1926.
20. R. Wright. A Short History of Progress. House of Anansi Press, 2004.

Chapter 4: Dynamic Systems
Further Reading Links:

Analysis: Dynamical system, Time series, Fourier transform, Wavelet transform<./a>, Principal components

Statistics: Correlation and Dependence, Correlation coefficient, Correlation and Causality, Stationary Process, Pearson’s Chi-Squared test

References:

1. G. Box, G. Jenkins, and G. Reinsel. Time series analysis: forecasting and control. Wiley, 4th edition, 2008.
2. C. Brase and C. Brase. Understanding Basic Statistics. Cengage Learning, 2012.
3. P. Brockwell and R. Davis. Introduction to Time Series and Forecasting. Springer, 2010.
4. R. Devaney. A First Course in Dynamical Systems. Westview Press, 1992.
5. R. Duda, R. Hart, and D. Stork. Pattern Classification. Wiley, 2000.
6. A. Ghosh. Dynamic Systems for Everyone: Understanding How Our World Works. Springer, 2015.
7. M. Kiemele. Basic Statistics. Air Academy, 1997.
8. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
9. A. Oppenheim, A. Willsky, and H. Nawab. Signals & Systems. Prentice Hall, 1997.
10. A. Papoulis and S. Pillai. Probability, Random Variables, and Stochastic Processes. McGraw Hill, 2002.
11. R. Robinson. An Introduction to Dynamical Systems. Prentice Hall, 2004.
12. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
13. E. Scheinerman. Invitation to Dynamical Systems. Dover, 2013.
14. P. Turchin. Complex Population Dynamics. Princeton, 2003.
15. P. Turchin. Historical Dynamics: Why States Rise and Fall. Princeton, 2003.
16. T. Urdan. Statistics in Plain English. Routledge, 2010.

Chapter 5: Linear Systems
Further Reading Links:

Linear system, Linear Time Invariant Systems Theory, Eigendecomposition, Jordan normal form, Control Theory

References:

1. B. Friedland. Control System Design: An Introduction to State-Space Methods. Dover, 2005.
2. Z. Gajic. Linear Dynamic Systems and Signals. Prentice Hall, 2003.
3. L. Gunderson and C. Holling. Panarchy: Understanding Transformations in Human and Natural Systems. Island Press, 2012.
4. C. Martenson. The Crash Course: The Unsustainable Future of our Economy, Energy, and Environment. Wiley, 2011.
5. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
6. M. Neubert and H. Caswell. Alternatives to resilience for measuring the responses of ecological systems to perturbations. Ecology, 78(3), 1997.
7. N. Nise. Control Systems Engineering. Wiley, 2015.
8. A. Oppenheim, A. Willsky, and H. Nawab. Signals & Systems. Prentice Hall, 1997.
9. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
10. E. Scheinerman. Invitation to Dynamical Systems. Dover, 2013.
11. L. Trefethen and M. Embree. Spectra and Pseudospectra: The Behaviour of Nonnormal Matrices and Operators. Princeton, 2005.
12. B. Walker and D. Salt. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, 2006.

Chapter 6: Nonlinear Dynamic Systems — Uncoupled
Further Reading Links:

Nonlinear Systems: Nonlinear System, Bifurcation theory, Hysteresis, Catastrophe Theory

Population: Population Dynamics, Carrying Capacity, Allee Effect, Predator-Prey Model

Climate Systems: Great Oxidation, Snowball Earth, Greenhouse and Icehouse Earth, Glacial Period, Milankovitch Cycles, Thermohaline Circulation, Little ice age, Medieval warm period

Other Papers: Varshney et al., The kinematics of falling maple seeds . . . , Nonlinearity (25), 2012
Andersen et al., Analysis of transitions between fluttering . . . , Fluid Mech. (541), 2005
H. Petroski, Engineering: Designed to Fail, American Scientist (85) #5, 1997

References:

1. K. Alligood, T. Sauer, and J. Yorke. Chaos: An Introduction to Dynamical Systems. Springer, 2000.
2. V. Arnol’d. Catastrophe Theory. Springer, 1992. 593 3. G. Deffuant and N. Gilbert (ed.s). Viability and Resilience of Complex Systems: Concepts, Methods and Case Studies from Ecology and Society. Springer, 2011.
4. L. Gunderson and C. Holling. Panarchy: Understanding Transformations in Human and Natural Systems. Island Press, 2012.
5. R. Hilborn. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford, 2000.
6. P. Loring. The most resilient show on earth. Ecology and Society, 12, 2007.
7. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
8. J. Rockström, W. Steffen, et al. Planetary boundaries: exploring the safe operating space for humanity. Ecology and Society, 14, 2009.
9. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
10. M. Scheffer, S. Carpenter, V. Dakos, and E. van Nes. Generic Indicators of Ecological Resilience: Inferring the Chance of a Critical Transition. Annual Reviews, 2015.
11. D. Sornette. Why Stock Markets Crash. Princeton, 2004.
12. S. Strogatz. Nonlinear Dynamics and Chaos. Westview Press, 2014.
13. P. Turchin. Complex Population Dynamics. Princeton, 2003.
14. B. Walker and D. Salt. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, 2006.

Chapter 7: Nonlinear Dynamic Systems — Coupled
Further Reading Links:

Nonlinear Systems: Nonlinear System, Hopf bifurcation, Limit cycle, Chaos theory

Economic Cycles: Goodwin Model, Business Cycle, Elliott Wave, Kondratiev Wave

Tragedy of the Commons: Tragedy of the Commons, Prisoner’s dilemma, Nash equilibrium
Hardin, The Tragedy of the Commons, Science (162), 1968
Ostrom, Governing the Commons, Cambridge, 2015

Examples: El Niño, La Niña, Lotka-Volterra Equation, Newton’s Method, Attractor, Fractal, Stick-Slip phenomenon

References:

1. K. Alligood, T. Sauer, and J. Yorke. Chaos: An Introduction to Dynamical Systems. Springer, 2000.
2. M. Crucifix. Oscillators and relaxation phenomena in pleistocene climate theory. Philosophical Transactions of the Royal Society A, 370, 2012.
3. G. Deffuant and N. Gilbert. Viability and Resilience of Complex Systems: Concepts, Methods and Case Studies from Ecology and Society. Springer, 2011.
4. P. Fieguth and A. Wong. Introduction to Pattern Recognition. Springer. (in preparation).
5. L. Gunderson and C. Holling. Panarchy: Understanding Transformations in Human and Natural Systems. Island Press, 2012.
6. R. Hilborn. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford, 2000.
7. P. Loring. The most resilient show on earth. Ecology and Society, 12, 2007.
8. D. Meadows. Thinking in Systems: A Primer. Chelsea Green, 2008.
9. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
10. M. Scheffer. Critical transitions in nature and society Princeton University Press, 2009.
11. M. Scheffer, S. Carpenter, V. Dakos, and E. van Nes. Generic Indicators of Ecological Resilience: Inferring the Chance of a Critical Transition. Annual Reviews, 2015.
12. S. Strogatz. Nonlinear Dynamics and Chaos. Westview Press, 2014.
13. B. Walker and D. Salt. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, 2006.
14. R. Wright. A Short History of Progress. House of Anansi Press, 2004.

Chapter 8: Spatial Systems
Further Reading Links:

Partial Differential Equations: Partial Differential Equation, Initial value problem, Boundary value problem, Discretization Finite element method

Earth Systems: Advection, Navier–Stokes, Coriolis effect, Low-pressure area, Ocean gyre, Buys Ballot’s law

Lumped Parameter Models: H. Stommel, Thermohaline Convection with Two Stable Regimes of Flow, Tellus (13) #2, 1961
H. Kaper, H. Engler, Mathematics & Climate, SIAM, 2013

Global Flows: Water cycle, Nitrogen cycle, Carbon cycle, Earth’s Energy Budget,
NASA Orbiting Carbon Observatory-2 (OCO-2)
NASA Clouds and the Earth's Radiant Energy System (CERES)

Cellular Automata and Agents: Cellular automaton, Conway’s Game of Life, Forest Fire model, Ising model, Agent-Based model
Simulation Environments: GAMA, NetLogo, StarLogo, Others

Traffic:
Wikipedia Links: Traffic flow, Traffic simulation, Three-phase traffic theory
Simulation Projects: ARCADY, ARCHISIM, CORSIM, MATSim

References:

1. J. Adam. Mathematics in Nature: Modeling Patterns in the Natural World. Princeton, 2006.
2. P. Bak. How Nature Works, Copernicus, 1996.
3. M. Batty. The New Science of Cities. MIT Press, 2013.
4. H. Dijkstra. Nonlinear Climate Dynamics. Cambridge, 2013.
5. L. Evans. Partial Differential Equations. American Mathematical Society, 2010.
6. S. Farlow. Partial Differential Equations for Scientists and Engineers. Dover Books, 1993.
7. B. Friedland. Control System Design. Dover, 2005.
8. J. Giles. Climate science: The dustiest place on earth. Nature, 434, 2005.
9. R. Hamming. Numerical Methods for Scientists and Engineers. Dover, 1987.
10. B. Hayes. Follow the money. American Scientist, 90(5), 2002.
11. H. Kaper and H. Engler. Mathematics & Climate. SIAM, 2013.
12. I. Koren et al. The Bodélé depression. Environmental Research Letters, 1, 2006.
13. R. Malone, R. Smith, M. Maltrud, and M. Hecht. Eddy–Resolving Ocean Modeling. Los Alamos Science, 2003.
14. D. Meadows, J. Randers, and D. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, 2004.
15. M. Mitchell. Complexity: A Guided Tour. Oxford, 2009.
16. A. Oppenheim, A. Willsky, and H. Nawab. Signals & Systems. Prentice Hall, 1997.
17. H. Peitgen, H. Jürgens, and D. Saupe. Chaos and Fractals: New Frontiers of Science. Springer, 2004.
18. B. Saltzman. Dynamical Paleoclimatology: Generalized Theory of Global Climate Change. Academic Press, 2001.
19. M. Schroeder. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Dover, 2009.
20. M. Sipser. Introduction to the Theory of Computation. Cengage Learning, 2012.
21. W. Strauss. Partial Differential Equations: An Introduction. Wiley, 2007.
22. S. Strogatz. Exploring complex networks. Nature, 410, 2001.
23. F. White. Fluid Mechanics. McGraw Hill, 2010.
24. S. Wolfram. A New Kind of Science. Wolfram Media, 2002.

Chapter 9: Power Laws and Non-Gaussian Systems
Further Reading Links:

Distributions: Normal Distribution, Central Limit Theorem, Exponential Distribution, Memorylessness, Poisson Distribution, Power law, Black swan, Heavy-Tailed Distributions

Power Laws: Zipf’s Law, Benford’s Law, Pareto Principle, Pareto Distribution, Gutenberg-Richter Law

Power Laws and Cities:
Bettencourt, The Origin of Scaling in Cities, Science (340), 2013
Bettencourt et al., Growth, innovation, scaling, and the pace of life in cities, PNAS (104), 2007

Discount Functions: Time preference, Time value of money, Hyperbolic discounting

Principles: Scale invariance, Scale-free network, Preferential attachment, Fitness model

References:

1. P. Bak. How Nature Works. Copernicus, 1996.
2. J. Diamond. Collapse: How Societies Choose to Fail or Succeed. Penguin, 2011.
3. B. Hayes. Follow the money. American Scientist, 90(5), 2002.
4. G. Lawler. Introduction to Stochastic Processes. Chapman & Hall, 2006.
5. R. Lowenstein. When Genius Failed: The Rise and Fall of Long-Term Capital Management. Random House, 2001.
6. D. Manin. Zipf’s law and avoidance of excessive synonymy. Cognitive Science, 32, 2008.
7. S. Resnick. Adventures in Stochastic Processes. Birkhäuser, 2002.
8. M. Schroeder. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Dover, 2009.
9. D. Sornette. Critical Phenomena in Natural Sciences. Springer, 2006.
10. M. Stumpf and M. Porter. Critical truths about power laws. Science, 335, 2012.
11. N. Taleb. The Black Swan: The Impact of the Highly Improbable. Random House, 2010.

Chapter 10: Complex Systems

Further Reading Links:

Complex Systems: Complex system, Phase transition, Critical phenomena, Critical point, Universality, Percolation theory, Network theory, Chaos theory

Self Organized Criticality: Self-organized Criticality, Self-organization, Emergence

Complex Behaviours: Swarm behaviour, Flocking

Control of Complex Systems:
D. Cajueiro, R. Andrade, Controlling self-organized criticality in sandpile models, Phys. Rev. E (81), 2010
P. Noël, C. Brummitt, R. D’Souza, Controlling Self-Organizing Dynamics on Networks Using Models that Self-Organize, Phys. Rev. Letters (111), 2013

Cascading Complex Systems:
W. Aiello, F. Chung, L. Lu, A random graph model for power law graphs, Experiment. Math. (10), 2001.
S. Buldyrev et al. Catastrophic cascade of failures in interdependent networks. Nature Physics, 464, 2010.
S. Rinaldi et al. Identifying, understanding, and analyzing critical infrastructure interdependencies. IEEE Control Systems Magazine, 21, 2001.
B. Carreras et al., Evidence for Self-Organized Criticality in a Time Series of Electric Power System Blackouts, IEEE Circuits and Sytems I (51), 2004
Dobson et al., Complex Systems Analysis of Series of Blackouts, Chaos (17), 2007
W. Kröger, E. Zio, Vulnerable Systems, Springer, 2011

Dictyostelium (Slime Mould): Dictyostelium, Overview, Tutorial, Sample Video

Resilience: Definitions, Stockholm Resilience Centre
J. Greer, Salvaging Resilience
P. Smith et al., Network Resilience: A Systematic Approach, IEEE Communications Magazine, 2011
Viability and Resilience of Complex Systems: Concepts, Methods and Case Studies from Ecology and Society. Springer, 2011.

References:

1. S. Arora and B. Barak. Computational Complexity: A Modern Approach. Cambridge, 2009.
2. P. Bak. How Nature Works. Copernicus, 1996.
3. P. Bak and K. Chen. Self-Organized Criticality. Scientific American, 1991.
4. Y. Bar-Yam. Dynamics of Complex Systems. Addison-Wesley, 1997.
5. S. Buldyrev et al. Catastrophic cascade of failures in interdependent networks. Nature Physics, 464, 2010.
6. R. Cohen and S. Havlin. Complex Networks: Structure, Robustness and Function. Cambridge, 2010.
7. G. Deffuant and N. Gilbert (ed.s). Viability and Resilience of Complex Systems: Concepts, Methods and Case Studies from Ecology and Society. Springer, 2011.
8. S. Dorogovtsev, A. Goltsev, and J. Mendes. Critical phenomena in complex networks. Reviews of Modern Physics, 80, 2008.
9. L. Fisher. The Perfect Swarm – The Science of Complexity in Everyday Life. Basic Books, 2009.
10. R. Frigg. Self-organised criticality — what it is and what it isn’t. Studies in History and Philosophy of Science, 34, 2003.
11. J. Gribbin. Deep Simplicity: Bringing Order to Chaos and Complexity. Random House, 2005.
12. H. Hoffmann and D. Payton. Suppressing cascades in a self-organized model with non-contiguous spread of failures. Chaos, Solitons, & Fractals, 67, 2014.
13. J. Holland. Complexity: A Very Short Introduction. Oxford, 2014.
14. S. Johnson. Emergence. Scribner, 2001.
15. M. Mitchell. Complexity: A Guided Tour. Oxford, 2009.
16. H. Peitgen, H. Jürgens, and D. Saupe. Chaos and Fractals: New Frontiers of Science. Springer, 2004.
17. S. Rinaldi et al. Identifying, understanding, and analyzing critical infrastructure interdependencies. IEEE Control Systems Magazine, 21, 2001.
18. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
19. M. Scheffer, S. Carpenter, V. Dakos, and E. van Nes. Generic Indicators of Ecological Resilience: Inferring the Chance of a Critical Transition. Annual Reviews, 2015.
20. M. Sipser. Introduction to the Theory of Computation. Cengage Learning, 2012.
21. S. Strogatz. Exploring complex networks. Nature, 410, 2001.
22. B. Walker and D. Salt. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, 2006.
23. S. Wolfram. A New Kind of Science. Wolfram Media, 2002.

Chapter 11: Observation and Inference
Further Reading Links:

Electromagnetics: Electromagnetic Radiation, Electromagnetic Spectrum, Scattering, Reflection (Physics), Radiative transfer, Planck’s law

Radar: Radar, Synthetic Aperture Radar, Interferometric Synthetic Aperture Radar

Remote Sensing: Remote Sensing, Satellite, List of orbits

Sensing Types: Microwave Radiometer, Scatterometer, Weather satellite, Altimeter

Sensing Platforms: Landsat program, Hubble Space Telescope, Radarsat-2, NASA Jason-2 Altimeter

Inverse Problems: Inverse Problem, Least Squares, Data Assimilation, Regularization, Medical Imaging

References:

1. R. Aster, B. Borchers, and C. Thurber. Parameter Estimation and Inverse Problems. Academic Press, 2005.
2. M. Bertero and P. Boccacci. Introduction to Inverse Problems in Imaging. Taylor & Francis, 1998.
3. A. Chandra and S. Ghosh. Remote Sensing and Geographical Information System. Alpha Science, 2015.
4. A. Tikhonov et al.. Numerical Methods for the Solution of Ill-Posed Problems. Kluwer Academic Publishers, 1995.
5. L. Kump et al.. The Earth System. Prentice Hall, 2010.
6. P. Fieguth. Statistical Image Processing and Multidimensional Modeling. Springer, 2010.
7. T. Lillesand, R. Kiefer, and J. Chipman. Remote Sensing and Image Interpretation. Wiley, 2015.
8. F. Mackenzie. Our Changing Planet. Prentice Hall, 2011.

Chapter 12: Water
Further Reading Links:

Ocean Acidification:
S. Doney, The Dangers of Ocean Acidification, Scientific American, 2006
E. Kolbert, The Acid Sea, National Geographic, 2011

Ocean Garbage: Marine Debris, Great Pacific Garbage Patch
L. Parker, Ocean Trash: 5.25 Trillion Pieces and Counting, National Geographic, 2015

Groundwater: Groundwater Recharge, Overdrafting, Ogallala Aquifer, Hydrogeology

References:

1. S. Grace. Dam Nation: How Water Shaped theWest and Will Determine Its Future. Globe Pequot Press, 2013.
2. S. Lovejoy and D. Schertzer. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge, 2013. 3. C. Roberts. An Unnatural History of the Sea. Harper Collins, 2009.
4. C. Roberts. The Ocean of Life. Viking, 2012.
5. M. Scheffer. Critical transitions in nature and society. Princeton University Press, 2009.
6. S. Solomon. Water: The Epic Struggle for Wealth, Power, and Civilization. Harper Collins, 2009.
7. M. De Villiers. Water: The Fate of Our Most Precious Resource. McClelland & Stewart, 2003.
8. A. Weisman. The World Without Us. Picador, 2007.

Chapter 13: Concluding Thoughts

References:

1. F. Capra and P. Luisi. The Systems View of Life: A Unifying Vision. Cambridge, 2014.
2. A. Ghosh. Dynamic Systems for Everyone: Understanding How Our World Works. Springer, 2015.
3. M. Mitchell. Complexity: A Guided Tour. Oxford, 2009.
4. M. Scheffer. Critical transitions in nature and society Princeton University Press, 2009.
5. A. Weisman. The World Without Us. Picador, 2007. 6. R. Wright. A Short History of Progress. House of Anansi Press, 2004.

Allendix A: Matrix Algebra

References:

1. D. Damiano and J. Little. A Course in Linear Algebra. Dover, 2011.
2. D. Lay, S. Lay, and J. McDonald. Linear Algebra and Its Applications. Pearson, 2014.
3. D. Poole. Linear Algebra: A Modern Introduction. Brooks Cole, 2014.

Appendix B: Random Variables and Statistics

References:

1. M. DeGroot and M. Schervish. Probability and Statistics. Pearson, 2010.
2. J. Haigh. Probability: A Very Short Introduction. Oxford, 2012.
3. R.Walpole, R. Myers, S. Myers, and K. Ye. Probability & Statistics for Engineers & Scientists. Pearson, 2006.