The Technion offers many of its mathematics courses, such as infinitesimal calculus and algebra, at several levels, with each course aimed at a different audience. At the lowest level are courses aimed at the “soft sciences”, such as biology, which usually need only elementary, practical calculations. In the middle sit the majority of the Technion’s students – the aspiring engineers, physicists, and computer scientists – who work with both down-to-earth and abstract math every day, but often get nauseous with stratospheric generalities. At the snobbish top sit the mathematics students (hi there!).
The following is a translation of a very clever Facebook post (originally in Hebrew; author unknown) explaining the difference between the various courses’ syllabuses using sandwiches.
Sandwich Making: Simple sandwiches of two bread slices, the Dripping Tomato Theorem. Compatible vegetables and incompatible vegetables. First and second order plastic bags. Associated fruit, olives, normal form and linear functionals on sandwiches.
Sandwich Making Eng.: Sandwiches of two and three bread slices. Murphy’s theorems (the Dripping Tomato, the Mixing Mayo, the Hard Avocado). Characteristics of vegetables, analytic and non-analytic vegetables, the vegetable compatibility function. Sandwich-storage solutions, plastic bags, paper bags, tearability, leakability and mushability in the backpack. Extra ingredients: Fruit, vegetables, the duality of the tomato. Canonical sandwich forms, the Triangular Sandwich Theorem, the Square Sandwich Theorem. Nontrivial bread: Nut bread, raisin bread, rye. Introduction to toast theory. Thermodynamics of cheese. Crispiness and solubility. Different toaster models: Toaster oven, waffle toaster, roller toaster. Numerical approximation of toast by sandwiches. Sandwich acquisition methods. Morning cake. Contraction of time and elongation of the bakery line.
Sandwich Making Sci.: Properties of a single bread slice. Linear combinations of multiple slices. Sides, spreads and vegetables. The definition of the sandwich. Annoyances while making sandwiches, sandwich analysis, the harmonic coefficient of the sandwich, taste calculations. External sandwich factors. Ideal insulators, approximation of ideal insulation, geometries of insulators, the topology of the sausage. Canonical forms of sandwiches and Caratheodory’s lemma for measurable sandwiches. Sandwiches using general bread.
Introduction to Sandwich Making: The concept of flour. The mixing homeomorphism, the Fixed Point Theorem, concepts from the Theory of Baking. Properties of general pastries. Vector analysis of pastries, the bread subspace, the pathology of the infinite baguette. Vegetable-growing over the field of the complex numbers. The maximal annoyance principle and its derivatives. Taste spaces, compatibility, incompatibility and independence. Constructing sandwiches using a straight-edge and compass. Canonical forms of sandwiches and existence theorems for normal subsandwiches of prime order. High dimensional sandwiches.
For the natives, here is the original image:
Cover photo by Marco Verch; see here for original.