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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2025--26--B term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Algebra 1 for CS

  \item[Course Number]
    \LRE{212‭.1‭.7011}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/spring2026/courses/algebra-1-cs}


\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{enumerate}
\item{} General background: sets and operations on them, Complex numbers: definition (via ordered pairs), addition and multiplication, inverses, adjoint, absolute value. Real and complex polynomials and their roots.
\item{} Fields: Definition, properties, examples: Rationals, reals, complex numbers, integers mod p.
\item{} Linear equations over fields, matrices and elementary row operations, rank of a matrix, solutions of homogeneous and non homogeneous systems of linear equations and the connections between them.
\item{} Vector spaces over fields, subspaces, bases and dimensions, coordinates change of coordinate matrix, row rank as rank of a subspace, sums, direct sums of subspaces and the dimension theorem.
\item{} Matrices multiplication, the algebra of square matrices, inverse determinants: properties, Cramer's rule, adjoint and its use for finding the inverse.
\item{} Linerar transformationsbasic propertieskernel and image of a linear trasformationrepresentaion of linear transformations by matrices and the effect of change of bases.linear functionals, dual bases
\end{enumerate}

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\end{document}

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