Read a calendar

Learning Objectives Model the day of the week as a function using modular arithmetic. Define the domain and range for calendar-based functions (e.g., days in a month, day of the year). Apply the concept of periodic functions to the 7-day week cycle. Construct a piecewise function to represent the number of days in each month. Represent recurring dates (e.g., every Tuesday) as an arithmetic sequence. Analyze and solve problems involving date calculations by applying function concepts. What day of the week will it be 1,000 days from today? 🗓️ Instead of counting, let's build a function to get the answer instantly! This lesson explores the familiar calendar through the advanced lens of mathematical functions. You will learn how concepts like domain, range, periodicity, an...

TermDefinitionExample FunctionA mathematical relation that maps each element from a set of inputs (the domain) to exactly one element in a set of outputs (the range).Let `M(d)` be a function where `d` is the date in January. `M(15)` maps to 'January 15th'. The input `15` has only one output. DomainThe complete set of all possible input values for a function.For a function `f(m)` that gives the number of days in a month `m` of a non-leap year, the domain is the set of integers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. RangeThe complete set of all possible output values of a function.For the function `f(m)` giving the number of days in a month of a non-leap year, the range is the set {28, 30, 31}. Modular ArithmeticA system of arithmetic for integers where numbers "wrap around...

Day-of-the-Week Function W(n) = (D_{start} + n) \pmod{7} Calculates the day of the week `n` days from a starting day. Let the days be indexed 0-6 (e.g., Sunday=0, Monday=1, ..., Saturday=6). `D_{start}` is the index of the starting day, and `n` is the number of days passed. The result `W(n)` is the index of the final day. Arithmetic Sequence of Dates d_k = d_1 + (k-1)p Finds the date of a specific day of the week within a month. `d_1` is the date of the first occurrence of that day (e.g., the first Tuesday), `p` is the period (always 7 for days of the week), and `k` is the occurrence number (e.g., 2nd, 3rd, 4th). `d_k` is the date of the k-th occurrence.