CS 7240: Topics and approximate agenda (Spring'24)
This schedule will be updated regularly as the class progresses. Check back frequently.
I will usually post lecture slides by the end of the day following a lecture (thus the next day), or latest two days after class.
Notice that I post one single slide deck for each unit (e.g. Topic 1  Unit 1 SQL), and I keep those slide decks updated as we progress with the unit across lectures.
I post them here on this website (or in Canvas if I think they are not yet ready to be released in public).
Please also check our DATA lab seminar for talks of interest.
Topic 1: Data Models and Query Languages

Lecture 1 (Tue 1/9):
Course introduction /
T1U1 SQL /
PostgreSQL setup /
SQL Activities

Lecture 2 (Fri 1/12):
T1U1 SQL

Lecture 3 (Tue 1/16) via Zoom:
T1U1 SQL

(Fri 1/19): no class

Lecture 4 (Tue 1/23):
T1U2 Logic & Relational Calculus

Lecture 5 (Fri 1/26):
T1U2 Logic & Relational Calculus

Lecture 6 (Tue 1/30):
T1U2 Logic & Relational Calculus /
T1U3 Relational Algebra & Codd's Theorem

Lecture 7 (Fri 2/2):
T1U3 Relational Algebra & Codd's Theorem

Lecture 8 (Tue 2/6):
T1U3 Relational Algebra & Codd's Theorem /
T1U4 Datalog & ASP

Lecture 9 (Tue 2/9):
T1U4 Datalog & ASP

(Tue 2/13): canceled due to snow emergency

Lecture 10 (Fri 2/16):
T1U4 Datalog & ASP

Lecture 11 (Tue 2/20):
T1U4 Datalog & ASP

Lecture 12 (Fri 2/23):
T1U4 Datalog & ASP

Lecture 13 (Tue 2/27):
T1U4 Datalog & ASP
Pointers to relevant concepts & supplementary material:

Unit 1. SQL:
[SAMS'12],
[CS 3200],
[Cow'03] Ch3 & Ch5,
[Complete'08] Ch6,
[Elmasri, Navathe'15] Ch6,
[Silberschatz+'20] Ch3.8

Unit 2. Logic & Relational Calculus:
FirstOrder Logic (FOL),
relational calculus (RC):
[Barland+'08] 4.1.2 & 4.2.1 & 4.4,
[Genesereth+] Ch6,
[Halpern+'01],
[Cow'03] Ch4.3 & 4.4,
[Elmasri, Navathe'15] Ch8.6 & Ch8.7,
[Silberschatz+'20] Ch27.1 & Ch27.2,
[Alice'95] Ch3.13.3 & Ch4.2 & Ch4.4 & Ch5.35.4,
[BarkerPlummer+'11] Ch11,
[Gatterbauer,Dunne'24]

Unit 3. Relational Algebra & Codd's Theorem:
Relational Algebra (RA),
Codd's theorem:
[Cow'03] Ch4.2,
[Complete'08] Ch2.4 & Ch5.15.2,
[Elmasri, Navathe'15] Ch8,
[Silberschatz+'20] Ch2.6,
[Alice'95] Ch4.4 & Ch5.4

Unit 4. Datalog & Answer Set Programming:
Datalog, recursion,
Stratified Datalog with negation,
Datalog evaluation strategies,
Stable Model semantics, Answer Set Programming (ASP):
[Complete'08] Ch5.3, [Cow'03] Ch 24,
[x755'19],
[Soufflé],
[Clingo], [Gatterbauer, Suciu'10], [Eiter+'09]

Unit 5. Alternative Data Models (not covered this year):
NoSQL:
[Hellerstein, Stonebraker'05], [Sadalage, Fowler'12], [Harrison'16]
Topic 2: Complexity of Query Evaluation & Reverse Data Management

Lecture 14 (Fri 3/1):
T2U1 Conjunctive Queries

Spring break (Tue 3/5, Fri 3/8)

Lecture 15 (Tue 3/12):
T2U1&2 Conjunctive Queries and Beyond

Lecture 16 (Fri 3/15):
T2U3 Provenance

Lecture 17 (Tue 3/19):
T2U3 Provenance

Lecture 18 (Fri 3/22):
T2U3 Provenance /
T2U4 Reverse Data Management
Pointers to relevant concepts & supplementary material:

Unit 1. Conjunctive Queries:
Query evaluation of conjunctive queries (CQs),
data vs. query complexity, homomorphisms,
constraint satisfaction, query containment,
query minimization, absorption:
[Kolaitis, Vardi'00], [Vardi'00],
[Kolaitis'16],
[Koutris'19] L1 & L2

Unit 2. Beyond Conjunctive Queries:
unions of conjunctive queries,
bag semantics,
nested queries,
tree pattern queries:
[Kolaitis'16],
[Tan+'14], [Gatterbauer'11], [Martens'17]

Unit 3. Provenance:
[Buneman+'02],
[Green+'07],
[Cheney+'09],
[Green,Tannen'17],
[Kepner+16],
[Buneman, Tan'18],
[Simons'23], [Dagstuhl'24]

Unit 4. Reverse Data Management:
update propagation, resilience:
[Buneman+'02],
[Kimelfeld+'12],
[Freire+'15],
[Makhija+'24]
Topic 3: Efficient Query Evaluation & Factorized Representations

Lecture 19 (Tue 3/26):
T3U1 Acyclic Queries

Lecture 20 (Fri 3/29):
T3U1 Acyclic Queries

Lecture 21 (Tue 4/2):
T3U1 Acyclic Queries

Lecture 22 (Fri 4/5):
T3U2 Cyclic Queries

Lecture 23 (Tue 4/9):
T3U2 Cyclic Queries

Lecture 24 (Fri 4/12):
T3U3 Factorized Representations,
T3U4 Optimization Problems & Topk
Pointers to relevant concepts & supplementary material:

Unit 1. Acyclic Queries:
query hypergraph, Yannakakis algorithm, GYO reduction,
dynamic programming, algebraic semirings,
[Alice] Ch6.4, [Koutris'19] L4,
enumeration, ranked enumeration:[Tziavelis+'20]

Unit 2. Cyclic Queries:
tree & hypertree decomposition,
query widths,
fractional hypertree width,
AGM bound,
worstcase optimal join algorithms,
optimal algorithms,
submodular width and multiple decompositions:
[AGM'13], [NPRR'18], [KNR'17], [KNS'17], [Gottlob+'16]

Unit 3. Factorized Representations:
normalization, factorized databases [Olteanu, Schleich'16]

Unit 4. Optimization Problems & Topk:
shortest paths, dynamic programming (DP),
Yannakakis, semirings,
rankings,
topk: [Roughgarden'10], [Ilyas+08], [Rahul, Tao'19],
ranked enumeration [Tziavelis+'20a], [Tziavelis+'20b], [TGR'22]
Topic 4: Linear Algebra & Iterative Graph Algorithms & Circuits

Lecture 25 (Tue 4/16):
T4U1 Graphs & Linear Algebra,
T4U2 Circuits & Computation Graphs

Lecture 26 (Fri 4/19):
T4U2 Circuits & Computation Graphs
Pointers to relevant concepts & supplementary material:

Unit 1. Graphs & Linear Algebra:
graphs,
linear algebra (LA),
semirings, iterative algorithms,
rankings on graphs,
associative arrays: [Lay+'21], [Kepner, Gilbert'11], [Kepner, Jananthan'18], [Klein'13],
Random walks & PageRank axioms: [Newman'10], [Gleich'15], [AT'10],
label propagation & backpropagation,
semisupervised learning [BDL'06],
factorized graph representations: [KLG'20],
belief propagation (BP): [Murphy'12], [GGKF'15]

Unit 2. Circuits & Computation Graphs:
circuits, knowledge compilation
[DM'02], [JS'13]
Topic 5: Normalization, Information Theory & Axioms for Uncertainty
Project presentations

Lecture 28 (Tue 4/23): P4 Project presentations

Lecture 29 (Fri 4/26): P4 Project presentations
Literature list
Topic 1: Data Models and Query Languages

Unit 1: SQL

[SAMS'19] SAMS: Teach yourself SQL in 10min by Forta. 5th ed. 2019.
It is available for free for Northeastern students
from Safari books eBook
(you may have to first login from our library website, then try again the previous link).
If the book is checked out online, you can use the 4th edition (there is almost no difference between 4th and 5th ed) as
Safari books eBook,
or as EBSCOhost eBook.

[CS 3200] PostgreSQL setup,
PgAdmin 4 tutorial.
Files to follow along our SQL lectures: SQL Activities,
CS 3200 web pages with more detailed slides on SQL.

[Cow'03] Ramakrishnan, Gehrke. Database Management Systems. 3rd ed 2003.
Ch 5: SQL.

[Complete'08] GarciaMolina, Ullman, Widom. Database Systems. 2nd ed 2008.
Ch 6: SQL.

[Elmasri, Navathe'15] Fundamentals of Database Systems. 7th ed 2015.
Ch 6: SQL

[Silberschatz+'20] Silberschatz, Korth, Sudarshan. Database system concepts. 7th ed 2020.
Ch 3.8: Nested subqueries.

Unit 2: Logic & Relational Calculus

[Barland+'08] Barland, Kolaitis, Vardi, Felleisen, Greiner.
Intro to Logic,
(alternative PDF version).
4.1.2 FirstOrder Logic: bound variables, free variables,
4.2.1 FirstOrder Logic: equivalences,
4.4 Exercises for FirstOrder Logic.

[Genesereth+] Genesereth et al. Introduction to logics.
Ch 6: Relational Logic.

[Halpern+'01] Halpern, Harper, Immerman, Kolaitis, Vardi, Vianu.
On the Unusual Effectiveness of Logic in Computer Science.
Bulletin of Symbolic Logic 2001.

[Cow'03] Ramakrishnan, Gehrke. Database Management Systems. 3rd ed 2003.
Ch 4.3: Relational calculus,
Ch 4.4: Safety.

[Elmasri, Navathe'15] Fundamentals of Database Systems. 7th ed 2015.
Ch 8.6: Tuple relational calculus,
Ch 8.7: Domain relational calculus,
Ch 8.6.8: Safe expressions.

[Silberschatz+'20] Silberschatz, Korth, Sudarshan. Database system concepts. 7th ed 2020.
Ch 27.1: Tuple relational calculus,
Ch 27.2: Domain relational calculus,
Ch 27.1.3 & 27.2.3: Safe expressions.

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 3.1: Structure of the relational model,
Ch 3.2: Named vs. unnamed perspective,
Ch 3.3: Conventional vs. logic programming perspective,
Ch 4.2: Logicbased perspective,
Ch 5.3: Relational calculus, domain independence,
Ch 5.4: Syntactic Restrictions for Domain Independence.

[BarkerPlummer+'11] BarkerPlummer, Barwise, Etchemendy. Language, Proof and Logic. 2nd ed. 2011.
Ch 11: Multiple Quantifiers.

[Vardi'13] A Logical Revolution (slides), 2013.
[Video @ MSR (1h 15min)]

[Gatterbauer,Dunne'24] On the Reasonable Effectiveness of Relational Diagrams: Explaining Relational Query Patterns and the Pattern Expressiveness of Relational Languages, SIGMOD 2014.

Unit 3: Relational Algebra & Codd's theorem

[Cow'03] Ramakrishnan, Gehrke. Database Management Systems. 3rd ed 2003.
Ch 4.2: Relational algebra.

[Complete'08] GarciaMolina, Ullman, Widom. Database Systems. 2nd ed 2008.
Ch 2.4: Relational algebra,
Ch 5.15.2: Relational Algebra and bags.

[Elmasri, Navathe'15] Fundamentals of Database Systems. 7th ed 2015.
Ch 8: Relational Algebra.

[Silberschatz+'20] Silberschatz, Korth, Sudarshan. Database system concepts. 7th ed 2020.
Ch 2.6: Relational algebra.

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 4.4: Algebraic perspectives,
Ch 5.35.4: Codd's theorem: Equivalence of algebra and calculus.

Unit 4: Datalog & Recursion

[Complete'08] GarciaMolina, Ullman, Widom. Database Systems. 2nd ed. 2008.
Ch 5.35.4: Datalog and bags,
Ch 10.2: Recursion in SQL.

[Cow'03] Ramakrishnan, Gehrke. Database Management Systems. 3rd ed 2003.
Ch 24.124.2: Datalog.

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 12.2: Datalog and modeltheoretic semantics,
Ch 12.3: Fixpoint semantics,
Ch 13.1: Seminaive evaluation,
Ch 15.2: Stratified semantics and precedence graphs

[Koutris'19] Lecture notes from CS784 Wisconsin 2019.
L9: Datalog evaluation,
L10: Datalog negation

[Gatterbauer, Suciu'10] Stable models: Gatterbauer, Suciu. Data conflict resolution using trust mappings.
SIGMOD 2010.
[PPTX slides],
[PDF slides],
[video (24min)]

[x775'19] x775 blog post: A surprisingly nice introduction to Datalog

[Soufflé] Soufflé is an opensource Datalog engine. Also see Soufflé tutorial and Soufflé installation. Soufflé files to follow along our lectures on Datalog with stratified negation:
Souffle Activities

[clingo] Postassco/Clingo is an is a disjunctive logic programming system, implementing the stable model semantics under the Answer Set Programming (ASP) paradigm. Download.
Running clingo in the browser,
More clingo resources.
Clingo files to follow along our lectures on ASP:
Clingo Activities.
Clingo user guide.

[Eiter+'09] Eiter, Ianni, Krennwallner. Answer Set Programming: A Primer. Reasoning Web International Summer School 2009.

Unit 5: Alternative Data Models

[Sadalage, Fowler'12] NoSQL Distilled: A Brief Guide to the Emerging World of Polyglot Persistence. 2012.
Safari books eBook(NEU free online access).
Ch 8: Keyvalue stoes,
Ch 9: Document databases,
Ch 10: Columnfamility stores,
Ch 11: Graph databases.

[Harrison'16] Next Generation Databases: NoSQL, NewSQL, and Big Data. 2016.
Safari books eBook (NEU free online access)].
p43p51: CAP, Eventual Consistency, Hashing,
p61p62: MongoDB,
p65p68: Graphs,
p75p80: Columns,
p145156: Data models,
p163, 164, 166: Secondary indexing.

[Stonebraker, Hellerstein'05] What Goes Around Comes Around. 2005.
Online PDF.
Also see various discussions of the paper.

[Kepner+'16] Kepner, Gadepally, Hutchison, Jananthan, Mattson, Samsi, Reuther. Associative Array Model of SQL, NoSQL, and NewSQL Databases. HPEC 2016.
Topic 2: Complexity of Query Evaluation & Reverse Data Management

Unit 1: Conjunctive Queries

[Chandra, Merlin'77] Optimal implementation of conjunctive queries in relational data bases. STOC 1977.

[Vardi'81] The Complexity of Relational Query Languages. STOC 1982.

[Vardi'00] Constraint satisfaction and database theory: a tutorial. PODS 2000.

[Kolaitis, Vardi'00]: ConjunctiveQuery Containment and Constraint Satisfaction. JCSS 2000.

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 2.1: Theoretical background,
Ch 6.2: Conjunctive queries & homomorphisms & query containment,
Ch 6.3: Undecidability of equivalence for calculus.

[Kolaitis'16]: Logic and Databases. Logical Structures in Computation Boot Camp, Berkeley 2016.
Firstorder logic as a database query language,
the query evaluation problem,
the query containment problem,
data complexity and combined complexity,
conjunctive queries.

[Koutris'19] Lecture notes from CS784 Wisconsin 2019.
L1: conjunctive queries,
L2: query containment.

Socratica on abstract algebra (Youtube):
why groups,
groups with examples,
Cayley tables for groups,
group homomorphisms,
group isomorphisms

3blue1brown on group homomorphisms (Youtube):
Euler's formula with introductory group theory,
Euler's number e

Unit 2: Beyond Conjunctive Queries

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 6.3: Undecidability of equivalence for calculus.

[Kolaitis'16]: Logic and Databases. Logical Structures in Computation Boot Camp, Berkeley 2016.
unions of conjunctive queries,
undecidability of query containment for unions of conjunctive queries.

[Tan+'14] Tan, Van den Bussche, Zhang. Undecidability of satisfiability in the algebra of ﬁnite binary relations with union, composition, and difference. Corr 1406.0349.

[Gatterbauer'11] Gatterbauer. Databases will visualize queries too. VLDB 2011.
Video,
Slides.

[Martens'17] Short summary of longer papers below Optimizing tree pattern queries: why cutting is not enough (invited talk). STOC 2017.
Czerwinski, Martens, Niewerth, Parys. Optimizing Tree Patterns for Querying Graph and TreeStructured Data. SIGMOD Record 2017.
Czerwinski, Martens, Niewerth, Parys. Minimization of Tree Patterns. JACM 2018.

Unit 3: Provenance

[Buneman+'02] Buneman, Khanna, Tan. On Propagation of Deletions and Annotations Through Views. PODS 2002.

[Cheney+'09] Cheney, Chiticariu, Tan. Provenance in databases: why, how, and where. Foundations and trends in databases 2009.

[Green+'07] Green, Karvounarakis, Tannen. Provenance Semirings. PODS 2007.

[Green, Tannen'17] PODS 2017 Test of Time Award: The Semiring Framework for Database Provenance. PODS 2017. (Slides).
See also:
Val Tannen's EDBT 2010 keynote: Provenance for Database Transformations. EDBT 2010.
Val Tannen's talk @ Logical Structures in Computation Boot Camp (including video):
Provenance for Database Transformations, Berkeley 2016.

[Kepner+'16] Kepner, Gadepally, Hutchison, Jananthan, Mattson, Samsi, Reuther. Associative Array Model of SQL, NoSQL, and NewSQL Databases. HPEC 2016.

[Buneman, Tang'18] Data Provenance: What next? SIGMOD Record 2018.

Socratica on abstract algebra (Youtube):
Rings with examples

[Gatterbauer+'11] Gatterbauer, Meliou, Suciu. Defaultall is dangerous! TaPP 2011.
(PPT Slides,
PDF Slides)

[Simons'23]: 2023 Simons semesterlong program on Logic and Algorithms in Database Theory and AI

[Dagstuhl'24]: 2024 Dagstuhl seminar on Representation, Provenance, and Explanations in Database Theory and Logic

Unit 4: Reverse Data Management

[Buneman+'02] Buneman, Khanna, Tan. On Propagation of Deletions and Annotations Through Views. PODS 2002.

[Kimelfeld+'12] Kimelfeld, Vondrak, Williams. Maximizing Conjunctive Views in Deletion Propagation. TODS 2012.

[Freire+'15] Freire, Gatterbauer, Immerman, Meliou. The complexity of resilience and responsibility for selfjoinfree conjunctive queries. PVLDB 2015.

[Freire+'20] Freire, Gatterbauer, Immerman, Meliou. New results for the complexity of resilience for binary conjunctive queries with selfjoins. PODS 2020.
(Video,
PPTX slides,
PDF slides)

[Makhija+'24] Makhija, Gatterbauer. A Unified Approach for Resilience and Causal Responsibility with Integer Linear Programming (ILP) and LP Relaxations. SIGMOD 2024.
(full version,
PDF slides,
Video)

[Meliou+'11] Meliou, Gatterbauer, Suciu.
Reverse data management.
PVLDB 2011 (challenges & vision track).

[Guidotti+'18] Guidotti, Monreale, Ruggieri, Turini, Giannotti, Pedreschi. A Survey of Methods for Explaining Black Box Models. ACM Computing Surveys 2018.
Topic 3: Efficient Query Evaluation & Factorized Representations

Unit 1: Acyclic Queries

[Yannakakis'81] Algorithms for acyclic database schemes. VLDB 1981.

[Bernstein, Chiu'81]
Bernstein, Chiu. Using semijoins to solve relational queries. JACM 1981.

[Bernstein, Goodman'81] Power of natural semijoins. SIAM J., 1981.

[Beeri+'83] Beeri, Fagin, Maier, Yannakakis. On the desirability of acyclic database schemes. JACM 1983.

[Alice'95] Abiteboul, Hull, Vianu. Foundations of Databases. 1995.
Ch 6.4: Acyclic joins, semijoin reduction, Yannakakis, GYO algorithm.

[Gottlob+'02] Gottlob, Leone, Scarcello. Hypertree Decompositions and Tractable Queries. JCSS 2002.

[Ullman'01] CS345 Lecture Notes. 2001.
Acyclic hypergraphs.
Computing acyclic joins, Yannakakis' algorithm.

[Koutris'19] Lecture notes from CS784 Wisconsin 2019.
L4: acyclic queries

[BraultBaron'16] Hypergraph Acyclicity Revisited. ACM Computing Surveys 2016

[TGR'22] Gatterbauer. Acyclic Queries & Enumeration (video). Part 3 of
Towards Responsive DBMS, ICDE 2022 tutorial.

[Graham'79] Graham.
On the Universal Relation (Technical Report).

Unit 2: Cyclic Queries

[AGM'13] AGM bound:Atserias, Grohe, Marx. Size bounds and query plans for relational joins. SIAM J. Comput. 2013.

[NPRR'18] WCO joins: Ngo, Porat, Re, Rudra. Worstcase optimal join algorithms. JACM 2018.

[KNR'17] FAQ: Khamis, Ngo, Rudra. Juggling functions inside a database. SIGMOD record 2017.

[KNS'17] Khamis, Ngo, Suciu. What do Shannontype inequalities, submodular width, and disjunctive Datalog have to do with one another? PODS 2017.

[Gottlob+'16] Gottlob, Greco, Leone, Scarcello. Hypertree Decompositions: Questions and Answers PODS 2016.

Unit 3: Factorized Representations

[Olteanu, Schleich'16] Factorized Databases. SIGMOD record 2016.

[Rendle'13] Scaling Factorization Machines to Relational Data. VLDB 2013.

[BCHDP'15] Bhattacherjee, Chavan, Huang, Deshpande, Parameswaran. Principles of Dataset Versioning: Exploring the Recreation/Storage Tradeoff. VLDB 2015.

[NNOS'18] Ngo, Nguyen, Olteanu, Schleich.
InDatabase Learning with Sparse Tensors. PODS 2018.

Socratica (Youtube): Abstract algebra: rings

[Kepner, Jananthan'18]. Mathematics of Big Data: Spreadsheets, Databases, Matrices, and Graphs. MIT press 2018.

Unit 4: Topk & Optimization Problems

[Fagin01] Fagin's algorithm: Fagin. Combining Fuzzy Information from Multiple Systems. JCSS 2001. (PODS 1996)

[Fagin+03] Threshold algorithm: Fagin, Lotem, Naor. Optimal aggregation algorithms for middleware. JCSS 2003. (PODS 2001)

[Roughgarden'10]: CS369N: Beyond WorstCase Analysis Lecture #1: Instance Optimality. Stanford 2010.

[Ilyas+08] Ilyas, Beskales, Soliman. A survey of topk query processing techniques in relational database systems. ACM Computing Surveys 2008.

[Rahul, Tao'19] Rahul, Tao. A Guide to Designing Topk Indices. SIGMOD record 2019.

[Tziavelis+'20a] Tziavelis, Ajwani, Gatterbauer, Riedewald, Yang. Optimal algorithms for ranked enumeration of answers to full conjunctive queries. PVLDB 2020. Project page.

[Tziavelis+'20b] Tziavelis, Gatterbauer, Riedewald. Optimal Join Algorithms meet Topk. SIGMOD tutorials 2020. Video tutorial,
Full tutorial page including slides.

[Gondran, Minoux'08]. Graphs, dioids and semirings: New Models and Algorithms. Springer 2008.

[Dijkstra'16]. Dijkstra’s Shortest Path Algorithm: an intuitive Youtube video.

[TGR'22] Gatterbauer. Dynamic Programming & Semirings (video). Part 5 of
Towards Responsive DBMS, ICDE 2022 tutorial.

[TGR'22] Tziavelis. Anyk or ranked enumeration (video). Part 6 of
Towards Responsive DBMS, ICDE 2022 tutorial.
Topic 4: Linear Algebra & Iterative Graph Algorithms

Unit 1: Graphs & Linear Algebra

[Kepner, Gilbert'11] Graph algorithms in the language of linear algebra. 2011.
Ch 1 (Graphs and Matrices), Ch 2 (Linear Algebraic Notations and Definitions), Ch 3 (Connected Components and Minimum Paths)

[Kepner, Jananthan'18] Mathematics of Big Data Spreadsheets, Databases, Matrices, and Graphs. 2018. (Online PDF).
Ch 6 (Manipulating Graphs with Matrices), 7 (Graph Analysis and Machine Learning Systems), 11 (Graph Construction and Graphical Patterns)

[Kepner+'18] Mathematics of Digital Hyperspace. IPDPSW 2021. (Online PDF).

[Easley, Kleinberg'10] Networks, crowds, and markets: reasoning about a highly connected world. 2010. Ch 14.6 (Spectral Analysis, Random Walks, and Web Search)

[3Blue1Brown]: 3Blue1Brown on Essence of linear algebra:
2. Linear combination, Span, Basis vectors,
7. Inverse matrices, column space, null space,
14. Eigenvectors, eigenvalues,
15. Abstract vector spaces

[Lay+'21]: Lay, Lay, McDonald. Linear algebra and its applications. 6th ed, 2021.
Ch 5 (Eigenvalues and Eigenvectors), Ch 10 (FiniteState Markov Chains)

[Meyer'01] Matrix analysis and applied linear algebra. SIAM. 2001.
Ch 7 (Eigenvalues)

[Klein'13] Coding the matrix: Linear Algebra through Applications to Computer Science. Newtonian Press. 2013. Online website with slides.
Ch 4 (The Matrix), Ch 10 (Special bases), Ch 11 (SVD), Ch 12 (The Eigenvector)

[Newman'10]: Networks: an introduction. Oxford University Press, 2010.
Ch 6 (Mathematics of networks), Ch 7 (Measures and Metrics)

[Gleich'15] PageRank beyond the Web, SIAM Review, 2015.

[AT'10] Altman, Tennenholtz. An axiomatic approach to personalized ranking systems, JACM, 2010.

[BDL'06] Bengio, Delalleau, Le Roux. Label Propagation and Quadratic Criterion. (book Ch 11 of "SemiSupervised Learning", 2006)

[Cowen+'17] Cowen, Ideker, Raphael, Sharan. Network propagation: a universal amplifier of genetic associations. Nature reviews, 2017.

[Murphy'12] Machine Learning: a Probabilistic Perspective, MIT press, 2012.
Ch 22.2 (Loopy belief propagation: algorithmic issues)

[Bishop'06] Pattern Recognition and Machine Learning, Springer, 2006.
Ch 8.4.4 (The Sumproduct algorithm), Ch 8.4.7 (Loopy belief Propagation)

[Huang'15] Online lecture on Belief Propagation by Bert Huang.

[Pearl'88] Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, 1988.
Ch 4 (Belief updating by network propagation)

[GGKF'15] Gatterbauer, Günnemann, Koutra, Faloutsos. Linearized and singlepass belief propagation. VLDB 2015. Youtube video.

[KLG'20] Kumar, Langton, Gatterbauer. Factorized Graph Representations for SemiSupervised Learning from Sparse Data. SIGMOD 2020. Youtube video.

[Doyle, Snell'84] Random walks and electric networks, 1984.
Ch 1.11.3 (Random walks on various networks)

[Minsky, Papert'88] Perceptrons, MIT press, 1988. Wikipedia page

Also see related past research seminar: Methods and Algorithms for determining relevance in networks (Fall'13).

Unit 2: Computation Graphs (Circuits & Knowledge Compilation)
Topic 5: Normalization, Information theory & Axioms of Uncertainty

Unit 1: Normal Forms & Information Theory

Unit 2: Axioms for Uncertainty
Research best practice
Surveys and additional possible topics