Introduction to Theory of Computation
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Power System Analysis and Design
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Computer Organization And Design: Hardware/Software Interface
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Algorithms
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Problem Solving with C++
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Starting Out with Python
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Starting Out with Programming Logic and Design
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Starting Out with Java: From Control Structures through Objects
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Starting Out With C++: Early Objects
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Starting Out With C++: From Control Structures through Objects
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Starting Out with Java: From Control Structures through Data Structures
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Relational Databases and Microsoft Access
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Computer Vision
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Foundations of Algorithms using C++ Pseudocode
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Foundations of Algorithms Using C++ Pseudocode
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Let \(V\) be a vector space over a field \(F\) and \(*: V \times V \longrightarrow F\) an inner product on \(V\). For a finite sequence \(a_{1}, \ldots, a_{n} \in V\) of vectors, let \(G=\left(a_{i} \star a_{j}\right) \in F^{n \times n}\) be the Gramian matrix of \(a_{1}, \ldots, a_{n}\). (i) Show that det \(G=0\) if and only if \(a_{1}, \ldots, a_{n}\) are linearly dependent. (ii) Conclude that the rank of \(G\) is equal to the rank of \(\left\\{a_{1}, \ldots, a_{m}\right\\}\).
How can you use an Intvar object to determine whether a checkbutton has been selected?
A simple undirected graph is complete if it contains an edge between every pair of distinct vertices. What does a depth-first search tree of a complete graph look like?
List five different types of Java programs.
Use the divide-and-conquer approach to write a recursive algorithm that finds the maximum sum in any contiguous sublist of a given list of \(n\) real values. Analyze your algorithm, and show the results in order notation.
