Tobias Homework

PACE Learning Center is excited to offer the families of Tobias Elementary School, an after school program that includes a Mandarin program, homework help and academic enrichment.


Enrollment in Tobias Chinese School is open year round and we warmly welcome students of all grades and ethnicity, and students with varying experiences with Mandarin.

(This program is open to non-Tobias students.)


Daily Schedule:

a)Mandarin Instruction - Classroom style teaching, focused on immersion and introduction of language and culture to spark interest in students so they want to learn more.

b)Homework Help - Tutors review and engage your child in their school's homework.

c) PACE Academic Enrichment - Extra teacher-approved worksheets are given to review and reinforce academic concepts.

d) Art and Recreation - A variety of art projects and team recreation allows students to express their creativity and active personalities.


Monthly Cost:

$295 After school till 6pm

$270 After school till 5pm

$185 Mandarin Only

+$100/year - supply fee

(includes Wednesday early pickup and minimum days)

additional discounts are available for prepayment of 1 or 2 payments


Questions, please call (415)952-7223 or email


The aim of this course will be to introduce the structural, operational approach to programming language semantics. It will show how this formalism is used to specify the meaning of some simple programming language constructs and to reason formally about semantic properties of programs and of tools like program analyzers and compilers. For the reasoning part the theorem prover Isabelle will be used.

At the end of the course students should
  • be familiar with rule-based presentations of the operational semantics of some simple imperative program constructs,
  • be able to prove properties of an operational semantics using various forms of induction and
  • be able to write precise formal proofs with the theorem prover Isabelle.

Important notice

  • You must be familiar with the basics of some functional programming language like Haskell, Objective Caml, Standard ML or F# (as taught, for example, in Introduction to Informatics 2 (IN0003)). For motivated students who do not have the necessary background yet: There are many introductions to functional programming available online, for example the first 6 chapters of Introduction to Objective Caml.
  • You must haven taken some basic course in discrete mathematics where you learned about sets, relations and proof principles like induction (as taught, for example, in Discrete Structures).
  • You need not be familiar with formal logic but you must be motivated to learn how to write precise and detailed mathematical proofs that are checked for correctness by a machine, the theorem prover Isabelle.
  • At the end of the course there will be a written or oral examination, depending on the number of students. Throughout the course there will be homework assignments. They will involve the use of Isabelle and will be graded. The final grade will be the better one of, a) your exam grade, b) a combined grade from the examination (60%) and the homework (40%).
  • All lectures are in English.

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