I suppose #1 and #3 should be working

test_many2many.clj

(ns mastermind.test.korma_test
  (:use korma.core
        korma.db
        clojure.test))

(defn connect-database []
  (let [config-map {:db "korma_test"
                    :user "postgres"
                    :password "postgres"
                    :host "localhost"
                    :port 5432}]
    (default-connection (create-db (postgres config-map)))))

(defn create-table []
  (exec-raw ["create table student (
                id varchar primary key,
                name varchar
                );"])
  (exec-raw ["create table course (
                id varchar primary key,
                name varchar
                );"])
  (exec-raw ["create table s_to_c (
                student_id varchar references student,
                course_id varchar references course
                );"]))

(defn drop-table []
  (exec-raw ["drop table s_to_c;"])
  (exec-raw ["drop table student"])
  (exec-raw ["drop table course"])
  )

(declare student course)

(defentity student
  (many-to-many course :s_to_c))

(defentity course
  (many-to-many student :s_to_c))

(defentity sc_relation
  (table :s_to_c))

(defn insert-data []
  (insert student (values {:id "1" :name "John"}))
  (insert student (values {:id "2" :name "Tim"}))
  (insert student (values {:id "3" :name "Immo"}))
  
  (insert course (values {:id "a" :name "Math"}))
  (insert course (values {:id "b" :name "English"}))
  (insert course (values {:id "c" :name "Chinese"}))
  
  (insert sc_relation (values {:student_id "1" :course_id "a"}))
  )

(use-fixtures :once (fn [f]
                      (connect-database)
                      (create-table)
                      (insert-data)
                      (f)
                      (drop-table)
                      ))

(deftest test-many-to-many []
  ;; test case #1
  (is (= (count (select student
                   (with course
                     (where {:name "Math"})))) 1) "Should this query return only one record?")
  ;; test case #2
  (is (= (count (select student
                   (with course
                     (where {:course.name "Math"})))) 1) "Should this query return only one record?")
  ;; test case #3
  (is (= (count (select student
                   (with course)
                   (where {:course.name "Math"}))) 1) "Should this query return only one record?"))

Ok, from the very beginning, I regard "with" as "join" in korma. I think this is the very first feeling for join table query from docs on sqlkorma.com/docs