MATH 107 - Technical Mathematics for the Information Age

Course Description

  • Prerequisite: "C" or higher in MATH 25 OR placement in MATH 27/103/107

A general survey of technical mathematics, with emphasis on the applications of mathematics to electronics, computers, and networking. Topics include: numbering systems for computers, Boolean algebra and logic gates for digital circuits, linear systems in three or more variables for DC circuits, trigonometry for AC circuits, exponential and logarithmic functions for AC circuits, rectangular and polar form of complex numbers for LRC circuits.

Student Learning Outcomes

Upon successful completion of Math 107, the student will be able to:

  • Represent base ten integers and decimal fractions as binary, octal, and hexadecimal numbers
  • Represent signed integers by 8-bit and 16-bit 2's complement numbers
  • Represent decimal numbers by binary codes, including the 8421, 4221, 5421, XS-3 codes, and Gray codes
  • Use truth tables and Boolean algebra to represent the actions of the logic gates AND, OR, NOT, NAND, NOR, XOR, and XNOR
  • Determine the maxterm and minterm expressions of a digital circuit from its truth table (perhaps including "don't cares") and simplification of the expressions via Karnaugh maps
  • Represent digital circuit logic diagrams by AND-OR logic, OR-AND logic, NAND logic, and NOR logic, including using DeMorgan's Laws to convert logic.
  • Solve linear systems in three unknowns and four unknowns by either substitution, addition, or Gauss-Jordan methods (depending on the instructor)
  • Evaluate rational exponents by hand and by calculator
  • Convert exponential and logarithmic equations, including manipulation of electronics formulas
  • Solve logarithmic equations that have a single logarithmic term
  • Graph exponential and logarithmic functions
  • Define the sine, cosine, and tangent trigonometric ratios for acute angles in a right triangle and for any angle in any quadrant, including positive and negative angles
  • Compute coterminal angles and reference angles
  • Convert degree and radian measure
  • Graph sine and cosine functions
  • Represent complex numbers on an Argand diagram, including using trigonometry to convert the rectangular and polar forms of complex numbers
  • Use the rectangular and polar forms of complex numbers to perform the operations of adding, subtracting, multiplying, dividing, raising to a power, and taking a root
  • Solve practical application problems, which may include linear systems in more than four unknowns, Kirchoff's Laws, reciprocal trigonometric ratios (secant, cosecant, and cotangent), transformations of the sine and cosine functions (phase shifting, changing the period, or changing the amplitude), or using complex numbers to model LRC circuits, depending on the instructor.

In general, the course will develop the student's quantitative-analytical reasoning abilities and will show the student how mathematics can be applied to electronics, computers, and networking.