MAC1105, College Algebra
Syllabus MAC1105 Class 10851
Miami Dade College, Kendall Campus.
Instructor: Carlos Sotuyo
email: csotuyo@mdc.edu
NYT, Richard Feynman: "Richard P. Feynman, arguably the most brilliant, iconoclastic and influential of the postwar generation of theoretical physicists (...)"
"My cousin, at that time, (...), was in high school and was having considerable difficulty with his algebra and had a tutor come, and I was allowed to sit in a corner while (LAUGHS) the tutor would try to teach my cousin algebra, problems like 2x plus something. I said to my cousin then, "What're you trying to do?" You know, I hear him talking about x. He says, "What do you know 2x + 7 =15," he says "and you're trying to find out what x is." I says, "You mean 4." He says, "Yeah, but you did it with arithmetic, you have to do it by algebra," and that's why my cousin was never able to do algebra, because he didn't understand how he was supposed to do it. There was no way. I learnt algebra fortunately by not going to school and knowing the whole idea was to find out what x was and it didn't make any difference how you did it, there's no such thing as, you know, you do it by arithmetic, you do it by algebra, that was a false thing that they had invented in school so that the children who have to study algebra can all pass it. They had invented a set of rules which if you followed them without thinking could produce the answer: subtract 7 from both sides, if you have a multiplier divide both sides by the multiplier and so on, and a series of steps by which you could get the answer if you didn't understand what you were trying to do."
Taken from The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman
Any fool can know. The point is to understand.
Albert Einstein.
The instrument that mediates between theory and practice, between thinking and observing, is mathematics. It builds the connecting bridge and makes it more and more noisy. Hence it is that our whole present culture, so far as it rests on the spiritual penetration and subservience of nature, finds its foundations in mathematics.
(...)
In fact, we do not master a scientific theory until we have peeled out its mathematical core and fully revealed it. Without mathematics, today's astronomy and physics are impossible. These sciences dissolve in their theoretical parts into mathematics.
David Hilbert
September 8, 1930 to the Society of German Scientists and Physicians in Königsberg.
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Fall of 2025, Miami Dade College
MWF 9:15 - 10:20 AM
Building 4, room 4207
9/22 Linear Equations.
Practice 01
9/24 Absolute Value Equations.
Practice 02
9/26 Linear Inequalities and Absolute Value Inequalities.
Practice 03
9/29 Definition of i, and Operations with Complex Numbers.
Practice 04
10/01 Solving Equations by Factoring.
Square Root Property and Completing the Square
Practice 05
10/03 Quadratic Formula
Solving Equations Quadratic in Form
Practice 06
10/06 Radical Equations.
Practice 07
10/08 Midpoint Formula, Distance Formula, and the Equation of a Circle
Practice 08
10/10 Test 1
10/13 Definition of Functions and their Graph
Functions and their Graph
Function Notation
Practice 09
10/15 Difference of Quotient
Identifying Even and Odd Functions
Finding the Domain of a Function
Practice 10
10/17 Library of Functions with Shifts
Reflection about the x-axis and y-axis, and Stretching and Shrinking
Practice 11
10/20 Piecewise Functions.
Practice 12
10/22 Composite of Functions and Operations on Functions
Practice 13
10/24 Finding the Inverse of a Functions.
Practice 14
10/27 Test 2
10/29 Sketching Quadratic Functions
Practice 15
10/31 Applications of Quadratic Functions
Practice 16
11/03 Definition of Polynomials and Sketching their Graphs
Practice 17
11/05 Vertical and Horizontal Asymptotes
Practice 18
11/07 Sketching Rational Functions
Practice 19
11/10 Polynomial and Rational Inequalities
Practice 20
11/12 System of Linear Equations Substitution Method
Practice 21
11/14 System of Linear Equations Addition Method
Practice 22
11/17 System of Inequalities
Practice 23
11/19 Test 3
11/21 Exponential Functions
Practice 24
11/24 Logarithmic Functions
Practice 25
11/26 Properties of Logarithms
Practice 26
12/01 Exponential Equations
Practice 27
12/03 Logarithmic Equations
Practice 28
12/05 Applications of Exponential Equations
Practice 29
12/08 Test 4
12/10 Final (optional)
12/12 Make-up exam
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