op" width=4 background="images/shadow.gif"></TD>
		
  <td valign="top" width="480"><p><font color="#FFFFFF" size="4"><strong>Algebra 
      (preparatory course)</strong></font><font color="#FFFFFF" size="3"><br>
      <strong>Mark Bashmakov</strong></font></p>
    <p><font color="#FFFFFF" size="3"><strong>Compex Numbers:</strong></font></p>
    <p><font color="#FFFFFF" size="3">General properties.Exponential form. Complex 
      roots of unity. Fundamental theorem of algebra. Applications of complex 
      numbers.</font></p>
    <p><font color="#FFFFFF" size="3"><strong>Fields:</strong></font></p>
    <p><font color="#FFFFFF" size="3">Characteristic of a field. Simple fields. 
      Algebraic extension. Field of rational functions.</font></p>
    <p><font color="#FFFFFF" size="3"><strong>Polynomials:</strong></font></p>
    <p><font color="#FFFFFF" size="3">Factorization. Irreducibility. Canonical 
      representation. Roots. Multiplicity. Interpolation formulas. Polynomials 
      in several variables. Ordering. Symmetric polynomials. Fundamental theorem 
      on symmetric polynomials. Sum of powers. Newton's formulas.</font></p>
    <p><font color="#FFFFFF" size="3"><strong>Rings:</strong></font></p>
    <p><font color="#FFFFFF" size="3">Commutative rings. Ideals. Quotient rings. 
      Maximal and prime ideals. Integral domains. Principal ideal domains. Unique 
      factorization domains. Euclidean domains. Construction of rings. Noetherian 
      rings. Hilbert basis theorem. Ring of Gaussian numbers.</font></p>
    <p><font color="#FFFFFF" size="3"><strong>Groups:</strong></font></p>
    <p><font color="#FFFFFF" size="3">Cyclic groups. Finite abelian groups. Finitely 
      generated abelian groups. Free abelian groups. Permutation groups. Altenating 
      groups. Groups acting on sets. Burnside's counting theorem. Group constructions. 
      Group extensions. Compositional series. Sylow's theorems. Automorphisms 
      of a group.</font></p>
    <p>&nbsp;</p></td>
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