Course Resources

Exams

Advanced Master's Exams (a.k.a. comps) Algebra 19960928 Algebra 20041105 Algebra 20050211 Algebra 2012 2 Algebra 2014 2 Complex 19951013 Complex 19970429 Complex 19980404 Complex 2003 / solutions Complex 2004 1 Complex 2004 2 Topology 19980227 Topology 20111207 MAT1093 - Precalculus MAT1093 Fall 2001 002 Final MAT1093 Fall 2001 002 Midterm 1 / solutions MAT1093 Fall 2001 002 Midterm 2 / solutions MAT1193 - Calculus for the Biosciences MAT1193 Fall 2011 005 Final / solutions MAT1193 Fall 2011 005 Midterm 1 / solutions MAT1193 Fall 2011 005 Midterm 2 / solutions MAT1193 Fall 2012 006 Final / solutions MAT1193 Fall 2012 006 Midterm 1 / solutions MAT1193 Fall 2012 006 Midterm 2 / solutions MAT1193 Fall 2012 007 Final / solutions MAT1193 Fall 2012 007 Midterm 1 / solutions MAT1193 Fall 2012 007 Midterm 2 / solutions MAT1193 Fall 2014 002 Final MAT1193 Fall 2014 002 Midterm 1 / solutions MAT1193 Fall 2014 002 Midterm 2 / solutions MAT1193 Fall 2014 002 Midterm 3 / solutions MAT1193 Fall 2014 003 Final MAT1193 Fall 2014 003 Midterm 1 / solutions MAT1193 Fall 2014 003 Midterm 2 / solutions MAT1193 Fall 2014 003 Midterm 3 / solutions MAT1193 Fall 2018 006 Midterm 1 / solutions MAT1193 Fall 2018 006 Midterm 2 / solutions MAT1194 Fall 2008 002 Final MAT1194 Fall 2008 002 Midterm 1 / solutions MAT1194 Fall 2008 002 Midterm 2 / solutions MAT1194 Fall 2009 001 Final / solutions MAT1194 Fall 2009 001 Midterm 1 / solutions MAT1194 Fall 2009 001 Midterm 2 / solutions MAT1194 Spring 2010 001 Final MAT1194 Spring 2010 001 Midterm 1 / solutions MAT1194 Spring 2010 001 Midterm 2 / solutions MAT1214 - Calculus I MAT1214 Spring 1995 002 Final MAT1214 Spring 1995 002 Midterm MAT1214 Spring 1996 001 Final MAT1214 Spring 1996 001 Midterm MAT1214 Spring 1996 003 Midterm MAT1214 Spring 1998 901 Final MAT1214 Spring 1998 901 Midterm 1 MAT1214 Spring 1998 901 Midterm 2 MAT1214 Spring 1998 901 Midterm 3 MAT1214 Spring 2000 901 Final MAT1214 Spring 2000 901 Midterm 1 MAT1214 Spring 2000 901 Midterm 2 MAT1214 Fall 2001 002 Final MAT1214 Fall 2001 002 Midterm 1 / solutions MAT1214 Fall 2001 002 Midterm 2 / solutions MAT1214 Fall 2001 002 Midterm 3 / solutions MAT1214 Spring 2002 001 Final MAT1214 Spring 2002 001 Midterm 1 MAT1214 Spring 2002 001 Midterm 2 MAT1214 Fall 2002 002 Final MAT1214 Fall 2002 002 Midterm 1 MAT1214 Fall 2002 002 Midterm 2 MAT1214 Fall 2003 005 Final MAT1214 Fall 2003 005 Midterm 1 MAT1214 Fall 2003 005 Midterm 2 MAT1214 Fall 2005 004 Final / solutions MAT1214 Fall 2005 004 Midterm 1 / solutions MAT1214 Fall 2005 004 Midterm 2 / solutions MAT1214 Spring 2006 009 Final / solutions MAT1214 Spring 2006 009 Midterm 1 / solutions MAT1214 Spring 2006 009 Midterm 2 / solutions MAT1214 Fall 2015 015 Midterm 1 / solutions MAT1214 Fall 2015 015 Midterm 2 / solutions MAT1224 - Calculus II MAT1223 Fall 1999 901 Final MAT1223 Fall 1999 901 Midterm 1 MAT1223 Fall 1999 901 Midterm 2 MAT1223 Fall 1999 901 Quizzes MAT1223 Spring 2003 002 Final MAT1223 Spring 2003 002 Midterm 1 MAT1223 Spring 2003 002 Midterm 2 MAT1223 Spring 2004 001 Final MAT1223 Spring 2004 001 Midterm 1 MAT1223 Spring 2004 001 Midterm 2 MAT1223 Spring 2006 005 Final / solutions MAT1223 Spring 2006 005 Midterm 1 / solutions MAT1223 Spring 2006 005 Midterm 2 / solutions MAT1224 Fall 2010 008 Midterm 1 / solutions MAT1224 Fall 2010 008 Midterm 2 / solutions MAT1313 - Algebra and Number Systems MAT1313 Spring 2022 002 Final / solutions MAT1313 Spring 2022 002 Midterm 1 / solutions MAT1313 Spring 2022 002 Midterm 2 / solutions MAT1313 Fall 2022 001 Final MAT1313 Fall 2022 001 Midterm 1 / solutions MAT1313 Fall 2022 001 Midterm 2 / solutions MAT1313 Spring 2023 001 Final MAT1313 Spring 2023 001 Midterm 1 / solutions MAT1313 Spring 2023 001 Midterm 2 / solutions MAT2214 - Calculus III MAT2213 Spring 1993 001 Final MAT2213 Spring 1993 001 Midterm 1 MAT2213 Spring 1993 001 Midterm 2 MAT2213 Fall 1993 001 Final MAT2213 Fall 1993 001 Midterm / solutions MAT2213 Fall 1993 002 Final MAT2213 Fall 1993 002 Midterm / solutions MAT2213 Spring 1994 003 Final MAT2213 Spring 1994 003 Midterm MAT2213 Spring 1994 005 Final MAT2213 Spring 1994 005 Midterm MAT2213 Fall 1997 001 Final MAT2213 Fall 1997 001 Midterm MAT2213 Fall 2004 002 Final MAT2213 Fall 2004 002 Midterm 1 MAT2213 Fall 2004 002 Midterm 2 MAT2213 Spring 2007 003 Final MAT2213 Spring 2007 003 Midterm 1 / solutions MAT2213 Spring 2007 003 Midterm 2 / solutions MAT2214 Fall 2014 003 Final / solutions MAT2214 Fall 2014 003 Midterm / solutions MAT2233 - Linear Algebra MAT2233 Spring 1999 001 Final MAT2233 Spring 1999 001 Midterm 1 MAT2233 Spring 1999 001 Midterm 2 MAT2233 Spring 1999 901 Final MAT2233 Spring 1999 901 Midterm 1 MAT2233 Spring 1999 901 Midterm 2 MAT2233 Fall 1999 001 Final MAT2233 Fall 1999 001 Midterm 1 MAT2233 Fall 1999 001 Midterm 2 MAT2233 Spring 2002 001 Final MAT2233 Spring 2002 001 Midterm 1 / solutions MAT2233 Spring 2002 001 Midterm 2 / solutions MAT2233 Fall 2002 001 Final / solutions MAT2233 Fall 2002 001 Midterm 1 / solutions MAT2233 Fall 2002 001 Midterm 2 / solutions MAT2233 Spring 2016 002 Final / solutions MAT2233 Spring 2016 002 Midterm 1 / solutions MAT2233 Spring 2016 002 Midterm 2 / solutions MAT2233 Spring 2016 002 Midterm 3 / solutions MAT2233 Fall 2016 002 Final / solutions MAT2233 Fall 2016 002 Midterm 1 / solutions MAT2233 Fall 2016 002 Midterm 2 / solutions MAT2233 Fall 2016 002 Midterm 3 / solutions MAT2233 Spring 2019 001 Midterm 1 / solutions MAT2233 Spring 2019 001 Midterm 2 / solutions MAT3013 - Foundations of Mathematics MAT3013 Spring 2012 002 Final / solutions MAT3013 Spring 2012 002 Midterm 1 / solutions MAT3013 Spring 2012 002 Midterm 2 / solutions MAT3013 Fall 2012 001 Final / solutions MAT3013 Fall 2012 001 Midterm 1 / solutions MAT3013 Fall 2012 001 Midterm 2 / solutions MAT3013 Fall 2015 002 Midterm 1 / solutions MAT3013 Fall 2015 002 Midterm 2 / solutions MAT3013 Spring 2020 001 Final / solutions MAT3013 Spring 2020 001 Midterm 1 / solutions MAT3013 Spring 2020 001 Midterm 2 / solutions MAT3013 Spring 2023 001 Final / solutions MAT3013 Spring 2023 001 Midterm 1 / solutions MAT3013 Spring 2023 001 Midterm 2 / solutions MAT3013 Fall 2023 001 Final MAT3013 Fall 2023 001 Midterm 1 / solutions MAT3013 Fall 2023 001 Midterm 2 / solutions MAT3013 Fall 2023 002 Final MAT3013 Fall 2023 002 Midterm 1 / solutions MAT3013 Fall 2023 002 Midterm 2 / solutions MAT3213 - Foundations of Analysis MAT3213 Spring 1998 001 Final MAT3213 Spring 1998 001 Midterm 1 / solutions MAT3213 Spring 1998 001 Midterm 2 MAT3213 Spring 1998 001 Midterm 3 MAT3213 Spring 2017 001 Final / solutions MAT3213 Spring 2017 002 Midterm 1 / solutions MAT3213 Spring 2017 002 Midterm 2 / solutions MAT3213 Spring 2018 001 Midterm 1 / solutions MAT3213 Spring 2018 001 Midterm 2 / solutions MAT3223 - Complex Variables MAT3223 Spring 1992 001 Final MAT3223 Spring 1992 001 Midterm 1 MAT3223 Spring 1992 001 Midterm 2 MAT3223 Spring 1994 001 Final MAT3223 Spring 1994 001 Midterm MAT3223 Spring 1998 001 Final MAT3223 Spring 1998 001 Midterm 1 MAT3223 Spring 1998 001 Midterm 2 MAT3223 Spring 1998 001 Midterm 3 MAT3223 Spring 2000 001 Final MAT3223 Spring 2000 001 Midterm 1 MAT3223 Spring 2000 001 Midterm 2 MAT3223 Spring 2002 001 Final MAT3223 Spring 2002 001 Midterm 1 / solutions MAT3223 Spring 2002 001 Midterm 2 / solutions MAT3223 Spring 2005 001 Final MAT3223 Spring 2005 001 Midterm 1 / solutions MAT3223 Spring 2005 001 Midterm 2 / solutions MAT3223 Spring 2005 001 Midterm 3 / solutions MAT3223 Spring 2009 001 Final MAT3223 Spring 2009 001 Midterm 1 / solutions MAT3223 Spring 2009 001 Midterm 2 / solutions MAT3233 - Modern Algebra MAT3233 Spring 2005 001 Final / solutions MAT3233 Spring 2005 001 Midterm 1 / solutions MAT3233 Spring 2005 001 Midterm 2 / solutions MAT3233 Fall 2010 001 Final / solutions MAT3233 Fall 2010 001 Midterm 1 / solutions MAT3233 Fall 2010 001 Midterm 2 / solutions MAT3233 Fall 2011 001 Final MAT3233 Fall 2011 001 Midterm 1 / solutions MAT3233 Fall 2011 001 Midterm 2 / solutions MAT3233 Spring 2015 001 Final / solutions MAT3233 Spring 2015 001 Midterm 1 / solutions MAT3233 Spring 2015 001 Midterm 2 / solutions MAT3233 Spring 2015 001 Midterm 3 / solutions MAT3243 - Calculus for Applications (vector calculus) * MAT3243 Fall 1994 001 Final MAT3243 Fall 1994 001 Midterm MAT3243 Fall 1995 001 Final MAT3243 Fall 1995 001 Final x MAT3243 Fall 1995 001 Midterm MAT3243 Fall 1996 001 Final MAT3243 Fall 1996 001 Final x MAT3243 Fall 1996 001 Midterm MAT3243 Fall 1997 001 Final MAT3243 Fall 1997 001 Midterm MAT3243 Fall 1997 001 Midterm x MAT3243 Fall 1998 001 Final MAT3243 Fall 1998 001 Midterm 1 MAT3243 Fall 1998 001 Midterm 2 MAT3243 Fall 1999 001 Final MAT3243 Fall 1999 001 Midterm 1 MAT3243 Fall 1999 001 Midterm 2 MAT3243 Fall 2001 001 Final MAT3243 Fall 2001 001 Midterm 1 / solutions MAT3243 Fall 2001 001 Midterm 2 / solutions MAT3243 Fall 2003 001 Final MAT3243 Fall 2003 001 Midterm 1 MAT3243 Fall 2003 001 Midterm 2 / solutions MAT3243 Fall 2004 001 Final MAT3243 Fall 2004 001 Midterm 1 / solutions MAT3243 Fall 2004 001 Midterm 2 / solutions MAT3243 Fall 2005 001 Final / solutions MAT3243 Fall 2005 001 Midterm 1 / solutions MAT3243 Fall 2005 001 Midterm 2 / solutions MAT3243 Fall 2007 001 Final / solutions MAT3243 Fall 2007 001 Midterm 1 / solutions MAT3243 Fall 2007 001 Midterm 2 / solutions MAT3243 Fall 2008 001 Final / solutions MAT3243 Fall 2008 001 Midterm 1 / solutions MAT3243 Fall 2008 001 Midterm 2 / solutions MAT3243 Fall 2009 001 Final / solutions MAT3243 Fall 2009 001 Midterm 1 / solutions MAT3243 Fall 2009 001 Midterm 2 / solutions MAT3253 - Engineering Analysis I * MAT3253 Fall 1993 001 Final MAT3253 Fall 1993 001 Midterm MAT3263 - Engineering Analysis II * MAT3263 Fall 1991 001 Final MAT3263 Fall 1991 001 Midterm 1 MAT3263 Fall 1991 001 Midterm 2 MAT3613 - Differential Equations I MAT3613 Fall 1995 001 Final MAT3613 Fall 1995 001 Midterm MAT3623 - Differential Equations II MAT3623 Spring 1992 i Final / solutions MAT3623 Fall 2006 001 Midterm 1 / solutions MAT3623 Fall 2006 001 Midterm 2 / solutions MAT3623 Spring 2016 001 Final / solutions MAT3623 Spring 2016 001 Midterm 1 / solutions MAT3623 Spring 2016 001 Midterm 2 / solutions MAT3623 Spring 2016 001 Midterm 3 / solutions MAT4213 - Real Analysis I MAT4213 Fall 1991 001 Final MAT4213 Fall 1991 001 Midterm 1 MAT4213 Fall 1991 001 Midterm 2 MAT4213 Fall 1992 001 Final MAT4213 Fall 1992 001 Final x MAT4213 Fall 1992 001 Midterm 1 MAT4213 Fall 1992 001 Midterm 2 MAT4213 Fall 1998 001 Final MAT4213 Fall 1998 001 Midterm 1 MAT4213 Fall 1998 001 Midterm 2 MAT4213 Fall 1998 001 Midterm 3 MAT4213 Fall 2016 001 Final / solutions MAT4213 Fall 2016 001 Midterm 1 / solutions MAT4213 Fall 2016 001 Midterm 2 / solutions MAT4213 Spring 2019 002 Midterm 1 / solutions MAT4213 Spring 2019 002 Midterm 2 / solutions MAT4223 - Real Analysis II MAT4223 Spring 1992 001 Final MAT4223 Spring 1992 001 Midterm 1 MAT4223 Spring 1992 001 Midterm 2 MAT4223 Spring 1993 001 Final MAT4223 Spring 1993 001 Midterm 1 MAT4223 Spring 1993 001 Midterm 2 MAT4233 - Modern Abstract Algebra MAT4233 Spring 2008 001 Final / solutions MAT4233 Spring 2008 001 Midterm 1 / solutions MAT4233 Spring 2008 001 Midterm 2 / solutions MAT4233 Spring 2009 001 Final / solutions MAT4233 Spring 2009 001 Midterm 1 / solutions MAT4233 Spring 2009 001 Midterm 2 / solutions MAT4233 Spring 2010 001 Final MAT4233 Spring 2010 001 Midterm 1 / solutions MAT4233 Spring 2010 001 Midterm 2 / solutions MAT4233 Spring 2011 001 Final MAT4233 Spring 2011 001 Midterm 1 / solutions MAT4233 Spring 2011 001 Midterm 2 / solutions MAT4233 Spring 2013 001 Final / solutions MAT4233 Spring 2013 001 Midterm 1 / solutions MAT4233 Spring 2013 001 Midterm 2 / solutions MAT4233 Spring 2015 001 Final / solutions MAT4233 Spring 2015 001 Midterm 1 / solutions MAT4233 Spring 2015 001 Midterm 2 / solutions MAT4233 Spring 2015 001 Midterm 3 / solutions MAT4233 Fall 2015 001 Final MAT4233 Fall 2015 001 Midterm 1 / solutions MAT4233 Fall 2015 001 Midterm 2 / solutions MAT4233 Spring 2017 001 Midterm 1 / solutions MAT4233 Spring 2017 001 Midterm 2 / solutions MAT4233 Fall 2017 001 Final / solutions MAT4233 Fall 2017 001 Midterm 1 / solutions MAT4233 Fall 2017 001 Midterm 2 / solutions MAT4233 Spring 2018 001 Midterm 1 / solutions MAT4233 Spring 2018 001 Midterm 2 / solutions MAT4233 Spring 2019 001 Final / solutions MAT4233 Spring 2019 001 Midterm 1 / solutions MAT4233 Spring 2019 001 Midterm 2 / solutions MAT4233 Fall 2019 001 Final / solutions MAT4233 Fall 2019 001 Midterm 1 / solutions MAT4233 Fall 2019 001 Midterm 2 / solutions MAT4233 Fall 2020 001 Final MAT4233 Fall 2020 001 Midterm / solutions MAT4233 Spring 2021 001 Final MAT4233 Spring 2021 001 Midterm / solutions MAT4233 Spring 2022 001 Final / solutions MAT4233 Spring 2022 001 Midterm / solutions MAT4233 Fall 2022 001 Final / solutions MAT4233 Fall 2022 001 Midterm / solutions MAT4253 - Number Theory MAT4253 Fall 2004 001 Final MAT4253 Fall 2004 001 Midterm 1 MAT4253 Fall 2004 001 Midterm 2 MAT4273 - Topology MAT4273 Fall 1997 001 Final MAT4273 Fall 1997 001 Midterm MAT4273 Spring 2022 001 Final MAT4273 Spring 2022 001 Midterm / solutions MAT4273 Spring 2023 001 Final MAT5173 - Algebra I MAT5173 Fall 1995 001 Final MAT5173 Fall 1995 001 Midterm MAT5173 Fall 2003 001 Final MAT5173 Fall 2003 001 Midterm 1 / solutions MAT5173 Fall 2003 001 Midterm 2 MAT5173 Fall 2013 001 Final / solutions MAT5173 Fall 2013 001 Midterm 1 / solutions MAT5173 Fall 2013 001 Midterm 2 / solutions MAT5223 - Theory of Functions of a Complex Variable I MAT5223 Fall 1992 001 Final MAT5223 Fall 1992 001 Final x MAT5223 Fall 1992 001 Midterm 1 MAT5223 Fall 1992 001 Midterm 2 MAT5223 Fall 1994 001 Final MAT5223 Fall 1996 001 Final MAT5223 Fall 1996 001 Midterm MAT5223 Fall 1998 001 Final MAT5223 Fall 1998 001 Midterm 1 MAT5223 Fall 1998 001 Midterm 2 MAT5223 Fall 2002 001 Final / solutions MAT5223 Fall 2002 001 Midterm 1 / solutions MAT5223 Fall 2002 001 Midterm 2 / solutions MAT5233 - Theory of Functions of a Complex Variable II MAT5233 Spring 1995 001 Final MAT5233 Spring 1997 001 Final MAT5233 Spring 1997 001 Midterm MAT5233 Spring 1999 001 Midterm 1 MAT5233 Spring 1999 001 Midterm 2 MAT5233 Spring 2003 001 Final MAT5233 Spring 2003 001 Midterm 1 MAT5233 Spring 2003 001 Midterm 2 MAT5243 - General Topology I MAT5243 Fall 1996 001 Final MAT5243 Fall 1996 001 Midterm MAT5243 Fall 2011 001 Midterm 1 / solutions MAT5243 Fall 2011 001 Midterm 2 / solutions MAT5253 - General Topology II MAT5253 Spring 1997 001 Final MAT5253 Spring 1997 001 Midterm MAT5263 - Algebraic Topology MAT5263 Spring 2013 001 Final / solutions MAT5263 Spring 2013 001 Midterm 1 / solutions MAT5263 Spring 2013 001 Midterm 2 / solutions MAT5313 - Algebra II MAT5313 Spring 1996 001 Final MAT5313 Spring 1996 001 Midterm 1 MAT5313 Spring 1996 001 Midterm 2 MAT5313 Spring 2004 001 Final MAT5313 Spring 2004 001 Midterm 1 / solutions MAT5313 Spring 2004 001 Midterm 2 / solutions MAT5313 Spring 2014 001 Final / solutions MAT5313 Spring 2014 001 Midterm 1 / solutions MAT5313 Spring 2014 001 Midterm 2 / solutions MAT5653 - Differential Equations I MAT5653 Fall 2016 001 Midterm 1 / solutions MAT5653 Fall 2016 001 Midterm 2 / solutions Math 450 (umich) - Advanced Engineering Mathematics Math 450 Spring 2001 002 Final Math 450 Spring 2001 002 Midterm 1 Math 450 Spring 2001 002 Midterm 2 CS3333 - Mathematical Foundations of Computer Science CS3333 Fall 2013 001 Final / solutions CS3333 Fall 2013 001 Midterm 1 / solutions CS3333 Fall 2013 001 Midterm 2 / solutions CS3333 Spring 2014 001 Final / solutions CS3333 Spring 2014 001 Midterm 1 / solutions CS3333 Spring 2014 001 Midterm 2 / solutions CS3333 Spring 2014 001 Midterm 3 / solutions CS3333 Fall 2014 001 Final / solutions CS3333 Fall 2014 001 Midterm 1 / solutions CS3333 Fall 2014 001 Midterm 2 / solutions CS3333 Fall 2014 001 Midterm 3 / solutions CS3333 Spring 2016 002 Final / solutions CS3333 Spring 2016 002 Midterm 1 / solutions CS3333 Spring 2016 002 Midterm 2 / solutions CS3333 Spring 2016 002 Midterm 3 / solutions * discontinued course