Instructions: First, select a category. Then, press the "Next
Question" button. Answer each question using the buttons A-G, then use
"Next Question" to move on to the next question. The quizzes are
completely anonymous, and do not directly affect your grades in any way;
however you may find the applet useful to identify any strengths or
weaknesses you have in various concepts in your courses.

Note: This applet does not work when advertisment-blockers are
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Comments, suggestions, and contributions for questions are greatly
appreciated, and will be acknowledged. When asking about a
specific question and answer, please quote the entire question and
answer, and not just the number of the question and label of the answer,
since question and answers may be shuffled within a quiz.

**important note:** these quizzes are no longer actively maintained on this site. The most recent version of these quizzes may be found here.

The following quizzes are currently on-line:

- Mathematical foundations (useful for any upper-division math course)
- Logic (17 questions). This tests the basics of mathematical logic, and in particular logical connectives (implication, negation, etc.) and quantifiers.
- Set theory (12 questions). This tests your knowledge of basic set theory operations such as union and intersection.
- Functions (10 questions). This tests your knowledge of basic properties of functions such as one-to-one, onto, and invertibility.
- Linear algebra, lower division (Math 33A)
- Linear systems (10 questions). This tests your knowledge on solvability of linear systems of equations.
- Elementary matrices (17 questions). This tests your knowledge on what the elementary matrix operations are.
- Vector Spaces (20 questions). This tests basic properties of vector spaces such as dimension, subspace, rank, linear independence, and so forth.
- Linear Transformations (15 questions). This tests basic characteristics of linear transformations such as null space, range etc.
- Determinants (12 questions). This tests knowledge of how the determinant is affected by basic matrix operations.
- Advanced matrices (7 questions). Questions on invertibilty, diagonalizability, etc.
- Linear algebra, upper division (Math 115A)
- Inner products (2 questions). This quiz needs more questions.
- Real Analysis (Math 131A)
- Sequences (26 questions). This quiz tests notions such as lim inf, lim sup, inf, sup, convergence, Cauchy convergence, boundedness, and limit points of sequences. You may find it quite challenging to get a perfect score!
- Countability (18 questions). This quiz tests your understanding of cardinality, and in particular the distinction between finite and infinite sets, and countable and uncountable sets.
- Inequalities (14 questions). Some questions about the arithmetic of inequalities, in particular testing your knowledge of the triangle inequality.
- Series (23 questions). Some questions about the conditional and absolute convergence of series, and the various tests for convergence.
- Continuity (14 questions). Some questions about limit points, adherent points, continuous functions, and uniformly continuous functions.
- Inf and Sup (13 questions). This tests your intuition on the infimum and supremum of sets of real numbers.
- Metric spaces (17 questions). This tests your knowledge of the basic definitions and concepts in the point set topology of metric spaces.
- Real Analysis, Graduate (Math 245)
- Measurable subsets of R (7 questions). Tests your knowledge on Borel sets, null sets, Lebesgue measurable sets, and so forth.
- Measures (9 questions). Tests your knowledge of countably additive measures.
- Modes of convergence (20 questions). Tests your knowledge of the various ways in which sequences of functions can converge.
- Fourier Analysis (Math 133)
- Convolutions (11 questions). This tests your knowledge on convolutions of periodic functions.
- Symmetries (15 questions). This tests your knowledge on the symmetries of the Fourier transform. (Note: some of the notation and material here is outside of the scope of Math 133).