Farzad Farnoud
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Mathematics of Information
1. Numbers, fields, and
representing information
Sets and set theory
Natural numbers, rationals
Fields
Real numbers
Counting and cardinality
Representing information
2. Probability & information
Defining information
Basics of probability
Random variables,
distributions, independence
Expectation and Variance
Conditional probability
Random sequences and
Markov chains
Quantifying Information
Data compression
Mathematics of communications
3. Linear algebra, finite fields,
and error correction
Codes, graphs, and algebra
Vectors and spaces
Fundamental spaces
Linear codes
4. The frequency domain and
transmission of information
Complex numbers
Frequency and spectrum
Filteration and sampling
Linear systems
Frequency response
Modulation
Orthogonality
Multiple-access communication
5. Number theory and
information privacy
Encryption
Number theory
Public key cryptography
6. Boolean algebra and
computation
Number systems and arithmetic
Boolean algebra
Logic design and computation
Appendix
Axiomatic systems
Frequency response