Core Math Crossword Puzzle
Across
- 2. A solution set is ___________ if its two solutions are linearly independent
- 6. Wolfram ___________ is a useful computational tool in Math 82
- 11. An undamped oscillator is an example of a ____________ system
- 12. We can use ________ expansion to compute the determinant of 3 x 3 matrices
- 14. A square matrix is __________ if and only if its determinant does not equal 0
- 16. The number of problem sets that we had in Math 82
- 18. An n x n matrix A is diagonalizable if and only if A has n linearly ___________ eigenvectors
- 19. The 2x2 zoology of phase portraits reminded us of the _____ emoji
- 21. We use the separation of variables method to solve first-order, _________ ODEs
- 22. A quantity that has both magnitude and direction
- 23. This type of circuit is mathematically similar to the mass-spring system with damping
- 28. An ___________ set is an orthogonal set of unit vectors
- 29. The instrument that Prof. Zinn-Brooks played in the Math 73 Music Video
- 34. The ___-Schwarz Inequality is |u・v| ≤ ||u|| ||v||
- 35. The dimension of a matrix’s null space
- 38. When using the Undetermined ___________ method to solve a forced, linear, constant-coefficient DE, we start by guessing a particular solution to the DE
- 39. The number of vectors in a basis for a subspace
- 40. An online space where we asked questions and collaborated with each other (in Math 19 & Math 82)
- 41. According to Prof. Jakes, ________ functions are the “peas and carrots” of DEs
- 42. The final step in the mathematical modeling process (based on Prof. Yong’s diagram)
- 43. We call two matrices row __________ if and only if they can be reduced to the same row echelon form
- 47. Describes a function that is injective AND surjective
- 50. An ____________ system of linear equations has no solution
- 51. “Very ______” - Prof. Karp
- 53. Another name for eᴬᵗ
- 54. The type of phase portrait that we obtain when the eigenvalues have real AND imaginary components
- 55. “Are you kidding, does this really ____?” - Prof. Jakes
- 56. The ________ Inequality is ||u + v|| ≤ ||u|| + ||v||
- 57. The dimension of a matrix’s row and column spaces
- 58. “______ is a rebellious lover.”
- 61. The Math 73 Music Video was a parody of “_____ the Sea” from The Little Mermaid
- 62. The ___________ matrix has columns that are linearly independent solutions of x’ = Ax
- 63. A center is a ______ equilibrium point
- 65. We can use elementary row operations to reduce a matrix into row _______ form
- 68. The last name of the other very important Darryl in Math 82
- 71. A technique that we use to solve nonlinear systems
- 74. y₁y₂’ − y₂y₁’
- 76. We find the ___________ points by setting x’ AND y’ equal to 0
- 77. In Math 19, we learned about single variable and multi variable ________
- 79. The Greek letter that we use to denote the fundamental matrix
- 80. Used as a prefix for “space”, “vector”, and “value”
- 83. The _____ Theorem states that an n x n real matrix is symmetric if and only if it is orthogonally diagonalizable
- 86. The _______-Grobman Theorem tells us when linearization is faithful
- 88. The _________ multiplicity of an eigenvalue is its multiplicity as a root of the characteristic equation
- 90. Cofactor expansion is also known as _______ expansion
- 91. The D in DE stands for ____________
- 92. Prof. Jakes always showed us a “ ___ of the day” after break
- 95. A fancier way of saying “onto”
- 96. x − x³/3! + x⁵/5! − ...
- 97. We can solve a non-separable, first-order, linear ODE using the ___________ factor method
- 98. To find the _________ of a matrix, we interchange the rows and columns of the matrix
- 101. Where all of our Core math courses took place
- 103. The ____ functions “even have their own Wikipedia page” - Prof. Yong & Prof. Jakes
- 104. We find the __________ by setting x’ OR y’ equal to 0
- 108. An online tool for graphing (useful for plotting level curves!)
- 113. In addition to being important in calculus, the ______ series are useful for solving DEs (especially when using the power series method)
- 116. An acronym for the epidemic model that we explored further in Math 82 (and were introduced to in Bio 52)
- 117. This type of ODE has a non-zero term that either depends only on the independent variable or is a non-zero constant
- 118. The first type of proof that we learned how to write (in Core math)
- 122. An unforced DE is also called a ___________ DE
- 123. An n x n matrix A is ______________ if there is a diagonal matrix D such that A is similar to D
- 126. The ____ of a set of matrices is the set of all linear combinations of the matrices
- 127. Like oscillations, ________ motion has damped and undamped DEs
- 128. A(BC) = (AB)C
- 129. The Greek letter that we use for eigenvalues and in the characteristic polynomial/equation
- 130. When we had questions in Math 73, we could post them on ______
- 131. The ______ form of a first-order, linear ODE is y’(x) + p(x)y(x) = q(x)
- 132. A _____ for a subspace is a set of vectors that spans the subspace and is linearly independent
Down
- 1. A square matrix is invertible if and only if ____ is not one of its eigenvalues
- 3. Our best guess to the solution of a DE (what we substitute into the DE to solve it)
- 4. The sum of the entries on the main diagonal of a matrix
- 5. Prof. Yong played us an adorable video of this animal at the end of each break
- 6. The password for Prof. Jakes’ (Math 82) Zoom meeting
- 7. The maximal interval over which a solution to a DE exists and satisfies the DE is the domain of _________
- 8. Our homework can either be handwritten or typed in _____
- 9. We learned about this type of polynomial of degree N while exploring power series
- 10. The professors that taught Math 82 during the summer of 2021 were Prof ____ and Prof Jakes
- 13. The _________ numbers are 1, 1, 2, 3, 5, 8, …
- 15. Statements that have been proven to be true (we reference these in the proofs that we write)
- 17. For a 2 x 2 matrix, we know this as “ad − bc”
- 20. An ________ point is the opposite of a singular point
- 24. A ________ is closed under addition and scalar multiplication
- 25. Used in Math 82 to describe a collection of phase portraits (although more commonly used to refer to the study of animals)
- 26. A __________ system of linear equations has at least one solution
- 27. The Gram-____ Process is an algorithm that we use to construct an orthogonal basis of a subspace of Rⁿ
- 30. A matrix of first-order partial derivatives that is often used for the linearization of nonlinear DEs
- 31. In this type of iteration, xₙ is an approximate solution to the DE
- 32. The highest number of derivatives that appears in an ODE
- 33. “Math 73, _______ to see”
- 36. A vector space that has no finite basis is _____-dimensional
- 37. The second step in the mathematical modeling process (based on Prof. Yong’s diagram)
- 44. We use the characteristic polynomial/equation to find the ___________ of a matrix
- 45. The type of problem that contains a DE and a boundary condition
- 46. The _________ multiplicity of an eigenvalue is the dimension of its corresponding eigenspace
- 48. The ______________ polynomial is a polynomial in λ obtained when expanding det(A − λI)
- 49. “The child of a theorem”
- 52. When x₀ is singular, we use the _________ method
- 59. Everyone’s favorite type of proof from Math 19 is the _______-delta proof
- 60. The highest rank that we reached in Prof Yong’s Spelling Bee game
- 61. A saddle is an ________ equilibrium point
- 64. When we solve a DE using power series, we find a _________ relation for the coefficients of a solution to the DE
- 66. The type of phase portrait that we obtain when the eigenvalues only have imaginary components
- 67. The last name of the author who wrote our Math 73 textbook
- 69. An acronym for the type of differential equations that we focused on in Math 82
- 70. Prof. Yong’s garage door is an example of a ______ oscillator
- 72. The type of problem that contains a DE and an initial condition
- 73. In ___ ODEs, the dependent variable and its derivatives only occur linearly
- 75. Prof. Jakes’ way of asking if something makes sense is saying this word twice
- 77. The set of all vectors that are orthogonal to a subspace is the orthogonal __________ of that subspace
- 78. We can use the _________ of parameters method to solve second-order, linear, forced ODEs
- 81. We use this website to submit our homework
- 82. An n x n matrix A is _______ to an n x n matrix B if there is an invertible n x n matrix P such that P⁻¹AP = B
- 84. Math 19, Math 73, and Math 82 are collectively known as ____ math
- 85. ________ and Feebas’ story taught us that “one must take risks in love”
- 87. A Greek letter that is commonly used with trig and polar coordinates
- 89. 1 − x²/2! + x⁴/4! − ...
- 93. In __________ ODEs, the independent variable does not appear explicitly
- 94. Everyone’s least favorite problem from (Math 82) Homework 4 was the _________ problem
- 99. ________ functions are infinitely differentiable
- 100. _____’s Method is a numerical tool that we used to approximate solutions to DEs
- 102. Matrix ______________ is not commutable
- 103. The corollary of ____’s Theorem says that the Wronskian of two solutions to a DE are either always zero or never zero
- 105. The broken furnace problem in (Math 82) Homework 6 relies on ______’s Law of Cooling
- 106. A square matrix is _________ if it equals its own transpose
- 107. Every higher order DE can be written as a ______ of first-order DEs
- 109. As Prof. Su often says, “You can’t ____ me from…”
- 110. When the determinant of A is negative, we’re in “______ city!”
- 111. A linear transformation that is both one-to-one and onto
- 112. Two vectors are __________ to each other if their dot product equals zero
- 114. As Prof. Orrison often says, “Change of ___________ is very important in math”
- 115. A ________ matrix is a square matrix whose non diagonal entries are all zeros
- 119. The Greek letter that we use for writing long sums
- 120. The solution to a forced DE consists of a homogeneous solution and a __________ solution
- 121. The third step in the mathematical modeling process (based on Prof. Yong’s diagram)
- 124. The type of phase portrait that we obtain when both eigenvalues are real and have the same sign
- 125. The ____ space is the subspace that contains solutions of the homogeneous linear system Ax = 0
- 126. A quantity that only has magnitude (no direction)